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By:-
DR. VIKRAM SINGHTANUSHREE SINGH
YEAR OF PUBLICATION-2010All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, transmitted in any form or by any means-
Electronic, Mechanical, Photocopying, Recording or otherwise, without
prior permission of the Authors and Publisher
SAVANT INSTITUTE
TM
CLASS XII
PHYSICS
Physics Ray Optics & Optical Instruments 1
SAVANT EDUCATION GROUP E-17, East of Kailash, New Delhi – 110065. Ph.: +91-11-26224417 www.savantgroup.org
§ Thin lens were first used for practical purposes by a Dutch merchant, Anton van Leeuwenhoek (1632 – 1723).
§ He used very small pieces of glass (it is easier to have a flawless small piece of glass than a flawless large one) and polished them so accurately that he could get magnifications of more than 200 without loss of detail.
§ He was able to see blood capillaries, and tiny living animals (protozoa).
§ The word telescope comes from the Greek “to see the distant.
§ The telescope is supposed to have been invented by an apprentice-boy in the shop of the Dutch spectacle maker Hans Lipershey (ca. (1570 – 1619) in about 1608.
§ Galileo Galilei (1564 – 1642), upon hearing rumors of the new device, experimented with lenses until he had built the first practical telescope in 1610.
Interactions between light and matter determine the appearance of everything around us: objects reflect some wavelengths, absorb others and emit others.
A women 1.60 m tall stands in front of a vertical plane mirror. What is the minimum height of the mirror, and how high must it lower edge be above the floor, if she is to see her whole body? (Assume her eyes are 10 cm below the top of her head.)
§ A plane mirror deviates light through an angle δ = 180° − 2i
§ Where i is the angle of incidence. The deviation is maximum for normal incidence. δmax = 180°.
§ Glancing angle φ = angle between mirror and reflected rays is called glancing angle φ = 90 – i = 90 – r.
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Slide 39
Rotation of Mirror
§ If the direction of the incident ray is kept constant and the mirror is rotated through an angle θ about an axis in the plane of mirror, then the reflected ray rotates through an angle 2θ.
§ If an object moves toward or away from) a plane mirror at speed v, the image will also approach (or recede) at the same speed v, and the relative velocity of image with respect to object will be 2v, as shown in figure a.
A man H m tall wishes to see his full-length image in a plane mirror hanging vertically on a wall. Find the length of the shortest mirror which he can see his entire image. If his eyes are H m above the ground, find the position of the mirror.
Rays parallel to the principal axis of the mirror come to a focus at F, called the focal point, as long as the mirror is small in diameter, d, as compared to its radius of curvature, r. In that case q will be small and the rays will cross each other at very nearly the same point.
(v) Focus (F) When a narrow beam of rays of light, parallel to the principal axis and close to it, is incident on the surface of a mirror, the reflected beam is found to converage or appear to diverge from a point on the principal axis. This point is called the focus .
(vi) Focal length (f) It is the distance between the pole and the principal focus. For spherical mirrors f = R/2
Reflection of light from spherical (curved) sign convention
§ Pole is taken to be the origin and the principal axis as the x-axis.
§ The quantities u, v, R and f is positive if the corresponding point lies on the positive side of the origin (in the direction of incident light) and negative if it is on the negative side. (opposite to the direction of incident light).
§ The distances measured in the upward direction, perpendicular to the principal axis of the mirror are taken as positive and those measured in downward direction is taken as negative.
§ The position, size and nature of an image formed by mirrors are conventionally expressed as ray diagrams. We can locate the image of any extended object graphically by drawing any two of the following four special rays: (a) A ray, initially parallel to the principal axis is reflected
through the focus of the mirror.
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Slide 56
(b) A ray, initially passing through the focus is reflected parallel to the principal axis.
(c) A ray passing through the centre of curvature is reflected back along itself.
(d) A ray incident at the pole is reflected symmetrically.
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Slide 73
Illustration
An object of length 3 cm is placed at a distance of (5/4)f from a concave mirror where f is the magnitude of the focal length of the mirror. The length of the object is parallel to the principal axis. Find the length of the image, is the image erect or inverted?
If the object and image distances are measured from the focus instead of the pole of the mirror. Then, the mirror formula reduces to a simple form called the Newton’s formula. x0 xi = f2 Where x0 is the object distance from the focus. xi is the image distance from the focus.
A short linear object is placed at a distance ‘u’ along the axis of a spherical mirror of focal length f. (i) Obtain an expression for the longitudinal magnification. (ii) Also, obtain an expression for the ratio of the velocity of
A small strip of plane mirror A is set with its plane normal to the principal axis of a convex mirror B and placed 15 cm in front of B which it partly covers. An object is placed 30 cm from A and the two virtual images formed by reflection in A and B coincide without parallax. Find the radius of curvature of B.
A concave mirror of focal length 15 cm) and a convex mirror (focal length 10 cm) are placed co-axially 70 cm apart facing each other. A 2 cm tall object is placed perpendicular to the common axis 20 cm from the concave mirror. Find the position, size and nature of the final image formed by two reflections, first at concave mirror and then at convex mirror.
Slide 78
Introduction:
Refraction through plane surface refraction of light
§ Refraction is a phenomena of light due to which it bends while travelling from one medium to another.
§ When light goes from one medium to another medium. ü Its velocity changes ü Its wavelength changes ü Its path may or may not change. ü Its frequency remains unchanged.
§ When light attempts to move from a medium having a given
index of refraction to one having a lower index of refraction.
Slide 92
§ As the incidence angle (θ1) is increased until a particular angle (θc), as shown in figure, the angle of refraction will be 90º and the refracted ray would skim the surface of the glass.
§ The incidence angle at which this occurs is called the critical angle, denoted as
Diamonds achieve their brilliance from a combination of dispersion and total internal reflection. Because diamonds have a very high index of refraction of about 2.4, the critical angle for total internal reflections only 25 degree. Incident light therefore strikes many of the internal surfaces before it strikes one at less than 25 degree and emerges. After many such reflections, the light has traveled far enough that the colors have become sufficiently separated to be seen individually and brilliantly by the eye after leaving the crystal.
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§ If µ2 > µ1, that is, when the object is observed from a denser medium, it appears to be farther away from the interface, i.e., y > x. or, Apparent height > Real height.
§ If µ2 < µ1, that is, when the object is observed from a rarer medium, it appears to be closer to the interface, i.e. y < x. i.e. Apparent depth < Real depth.
Note:
§ The above formula is only applicable for normal view or paraxial ray assumption.
§ For an angle of incidence greater than θc, the light is totally reflected back into the medium of higher refractive index. This phenomenon is called total internal reflection.
§ The optical fibres can transmit light beam from one end to the other due to the repeated total internal reflections even if the fiber is bent or twisted.
§ The refracting surfaces of a glass slab are parallel to each other. When a light ray travels through a glass slab, it is refracted twice at the two parallel faces and finally emerges out parallel to its incident direction.
§ The light ray undergoes zero deviation, δ = O. § Angle of emergence = Angle of incidence
When a glass slab of thickness t and refractive index µ is placed in the path of a convergent beam as shown in the figure, then the point of convergence is shifted by
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§ If there are n number of slabs with different refractive indices are placed between the observer and the object, then the total apparent shift is equal to the summation of the individual shifts.
In the figure, determine the apparent shift in the position of the coin. Also, find the effective refractive index of the combination of the glass and water slab.
Slide 129
Prism
§ Prism is a transparent medium with two refracting surfaces through which refraction takes place.
§ The two faces are not parallel but are inclined to each other.
§ Any geometrical figure with two refracting surfaces are not parallel in a prism.
A rectangular block of refractive index µ is placed on a printed page lying on a horizontal surface as shown in the figure. Find the minimum value of µ so that the letter L on the page is not visible from any of the vertical sides.
A ray of light PQ is incident at an angle i on face ML of a prism and is refracted along OR (figure). This ray, after refraction at face MN, travels along RN at grazing emergence. If µ is the refractive index and A refracting angle of the prism, show that
§ Object is a point object lying on the principle axis. § The incident and the refracted rays make small angles with
the principal axis. § The aperture is small.
Slide 153
Mathematical expression of Refraction at spherical surface
§ Two media of refractive index µ1 and µ2, when separated by a transparent curved surface, can be regarded as the case of refraction at spherical surface.
Refraction at a spherical surface separating two media
§ The figure shows how light refracts at the interface of two curved media.
§ C is the centre of curvature of medium ‘2’. § CN is the normal to the curved surface and § O is the point where the object lies. § After refraction, let the image be formed at I. § Let ‘u’ be the object distance, and ’v’ be the image distance.
A convex refracting surface of radius of curvature 15 cm separates two media of refractive indices 4/3 and 1.5. An object is kept in the first medium at a distance of 240 cm from the refracting surface. Calculate the position of the image.
An empty spherical flask of diameter 30 cm is Placed in water of refractive index. A parallel beam of light strikes the flask. Where does it get focused, when observed from within the flask?
What curvature must be given to the bounding surface of a refracting medium (µ = 1.5) for the virtual image of an object in the adjacent medium (µ = 1) at 10 cm to be formed at a distance of 40 cm?
§ The geometry of image formation by a double convex lens. § The first refracting surface forms the image I1 of the object O. § The image I1 acts as a virtual object for the second surface
A convex lens is to be used to throw on a screen 10 cm from the lens, a magnified image of an object. If the magnification is to be 19, find the focal length of the lens.
§ It is a beautiful patterns of colours seen in the sky after a shower
§ The rainbow is an example of the dispersion of sunlight by the water drops in the atmosphere.
§ The conditions for observing a rainbow are that the sun should be shining in one part of the sky while it is raining in the opposite part of the sky.
Slide 196
Primary rainbow
§ The primary rainbow has violet colour on the inner edge and the red colour on the outer edge of the rainbow.
§ Primary rainbow is formed due to two refractions and one total internal reflection of the light incident on the droplets.
§ Rests on a layer of tears between it and the cornea § Produces the same result as eyeglasses § Most refraction occurs at air-lens surface where change in
refractive index is greatest.
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§ A person who can see distant objects clearly but cannot focus on near objects clearly is farsighted.
§ This defect may occur if the diameter of person’s eyeball is smaller than usual.
§ In such a case, for an object placed at the normal near point (i.e., 25 cm from eye), the image of the object is formed behind the retina as shown in fig.
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Slide 214
Correction
To correct for long sighted vision a converging lens of suitable focal length is placed in front of the eye.
§ It is a defect in which eye lens looks at a wire eye mesh or a grid of lines, focusing in either the vertical or the horizontal plane which may not be as sharp as in the other plane.
§ ‘It is caused due to the non-uniformity in the spherical shape of the cornea.
§ It can be corrected using a cylindrical lens of desired radius of curvature with an appropriately directed axis.
Note
§ Astigmatism can occur along with myopia or hypermetropia.
Far point of a short-sighted person is 100 cm. What lens should he use to see distant objects clearly?
Slide 218
Solution
Since the far point of the short-sighted person is 100 cm away, he can see objects situated up to a distance of 100 cm. so, the lens used should be such that it forms the image (virtual) of the distant object at a distance of 100 cm. ∴ u = – ∞, v = – 100 cm
§ Luminous intensity of source in a given direction is defined as the luminous flux per unit solid angle in that direction.
§ The unit of luminous intensity is candela (cd). § Candela is defined as the luminous intensity, in a given
direction, of a source that emits monochromatic radiation of frequency 5.40 × 1014 Hz and that has a radiant intens ity in the direction of watt per steradian.
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§ Illuminance or Intensity of illumination of a surface at any point may be defined as the luminous flux incident normally on a unit area of the surface held at that point.
§ It is generally denoted by E. § If luminous flux ∆φ falls normally on an area ∆A of a surface,
It is an optical instrument used to see small and minute particles.
Slide 227
Magnifying power of a simple microscope
The angular magnification or magnifying power of a simple microscope is the ratio of the angle subtended at the eye by the image at the near point and the angle subtended at the unaided eye by the object at the near point.
§ Both types of telescope can suffer from a defect called spherical aberration so that not all of the light is focused to the same point.
§ This can happen if the mirror is not curved enough (shaped like part of a sphere instead of a paraboloid) or the glass lens is not shaped correctly.
Slide 240
§ The Hubble Space Telescope objective suffers from this (it is too flat by 2 microns, about 1/50 the width of a human hair) so it uses corrective optics to compensate.
§ The corrective optics intercept the light beams from the secondary mirror before they reach the cameras and spectrographs. Fortunately, the Hubble Space Telescope's spherical aberration is so perfect, that it is easy to correct for!
§ Angular magnification or magnifying power of a compound microscope is defined as the ratio of the angle subtended by the final image at the eye to the angle subtended by the object seen directly, when both are placed at the least distance of distinct vision.
§ These are optical instruments used to observe distant objects.
§ It has an objective and an eyepiece, the objective has a large focal length and a much larger aperture than the eyepiece.
§ Light from a distant object enters the objective and a real image is formed in the tube at its second focal point.
§ The eyepiece magnifies this image producing a final inverted image.
Slide 277
Magnifying power of a telescope
Magnifying power of a telescope m is the ratio of the angle β subtended the eye final image to the angle α which the object subtends at the lens or the eye.
§ The ability of an optical instrument to produce distinctly
separate images of two objects very close together is called resolving power of the instrument.
§ It depends on the diameter of the objective lens.
CURRICULUM BASED WORKSHEET
Topics for Worksheet – I
Reflection of light on plane and curved surface
Worksheet – I
1. A small candle 2.5 cm in size is placed 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to receive a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
2. An object is placed in front of a convex mirror of focal length 60 m. If image formed is half of its size, find the position of image.
3. A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length 10 cm. What is the area enclosed by the image of the wire? Given: the centre of the wire is on the axis of the mirror, with its two sides normal to the axis.
4. An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between, so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object, find the radius of curvature of the convex mirror.
5. A man 2 m tall, whose eye level is 1.84 m above the ground, looks at his image in a vertical mirror. What is the minimum vertical length of the mirror if the man is to be able to see the whole of himself?
6. Find the position of an object which when placed in front of a concave mirror of focal length 20 cm produces a virtual image which is twice the s ize of the object.
7. An object is placed (i) 10 cm (ii) 5 cm in front of a concave mirror of radius of curvature 15 cm. Calculate the position, nature and magnification of the image in each case.
8. An object is placed 15 cm from a convex mirror of radius of curvature 90 cm. Calculate image position and magnification.
9. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
10. An object is placed in front of a concave mirror of radius of curvature 40 cm at a distance of 10 cm. Find the position, nature and magnification of the image.
11. An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, by how much distance is the image displaced.
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Topics for Worksheet – II
Refraction on a plane surface
Worksheet – II
1. A ray of light of frequency of 5 × 104 Hz is passes through a liquid. The wavelength of light measured inside the liquid is found to be 450 × 10−9m. Calculate the refractive index of the liquid.
2. A tank is filled with water to a height of 12.5 cm. The apparent depth of a meddle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance would the microscope have to be moved to focus on the needle again?
3. A small pin fixed on a table top is viewed from above from a distance of 50 cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15 cm thick glass slab held parallel to the table? Refractive index of glass = 1.5. Does the answer depend on the location of the slab?
4. Velocity of light in a liquid is 1.5 × 108 m s−1 and air, it is 3 × 108 m s −1. If a ray of light passes from this liquid into air, calculate the value of critical angle. *This explains the plane: Total internal Reflection.
5. A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. [Consider the bulb to be a point source of light.]
6. Velocity of light in glass in 2 × 108 m s−1 and that in air is 3 × 108 m s −1. By how much would an ink dot appear to be raised when covered by a glass plate 6 cm thick?
7. The bottom of a container is 4.0 cm thick glass (µ = 1.5) slab. The container contains two immiscible liquids A and B of depths 6.0 cm and 8.0 cm respectively. What is the apparent position of a scratch on the outer surface of the bottom of the glass slab when viewed through the container? Refractive indices of A and B are 1.4 and 1.4 respectively.
8. Refractive index of glass 1.5. Calculate velocity of light in glass if velocity of light in vacuum is 3 × 108 m s−1. Also calculate critical angle for glass-air interface.
9. Determine the critical angle for a glass-air surface, if a ray of light which is incident in air on the surface is deviated through 15°. When its angle of incidence is 40°.
10. Fig. shows a triangular prism of glass. A ray incident normally on one face is totally reflected. What can you
conclude about the minimum value of index of refraction of glass?
11. (a) Fig. shows a cross-section of a light-pipe made of
glass fibre of refractive index 1.68. The outer covering of the pipe is made of a material of refractive index 1.44. What is the range of the angles of incident easy with the axis of the pipe for which total reflections inside the pipe take place as shown in Fig.
(b) What is the answer if the is no outer covering of the pipe?
Topics for Worksheet – III
Prism
Worksheet – III
1. Parallel light from the collimator of a spectrometer is incident on the two faces of a prism which make the refracting angle A of the prism. The image of the collimator slit is observed in two different positions of the telescope of the spectrometer. If the angle of rotation of the telescope between the two positions is 144°, what is the angle A of the prism?
2. For a given source of light, the angle of minimum deviation of a 60° prism is 56°. What is its refractive index?
3. If the refractive index of the material of a prism of refracting angle 8° is 1.532 for blue red light, what is the angular dispersion produced by the prism?
4. A ray of light passes through an equilateral prism (µ = 1.5) such that angle of incidence is equal to angle of
emergence and the latter is equal to 3
th4
of the angle
of prism. Calculate the angle of deviation. 5. A ray of light passes through an equilateral glass prism
such that the angle of incidence is equal to the angle of
emergence. The angle of emergence is 34
times the
angle of prism. Calculate the refractive index of the glass prism.
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6. Using a spectrometer, the following data are obtained for a crown glass prism and a flint glass prism. Angle of the prism, A = 72.0° Minimum deviation angle, δb = 54.6°, δr = 53.0°, δy = 54.0° Flint glass prism: A = 60.0°, δb = 52.8′, δr = 50.6 ° δy = 51.9 ° b, r and y refer to particular wavelengths in the blue, red and yellow bands. Compare the dispersive powers of the two varieties of glass prisms.
7. Find the angle of flint glass prism which produces the same angular dispersion for C and F wavelengths as a 10° crown glass prism. For crown glass: µF = 1.5230, µC = 1.5145 For flint glass: µF = 1.6637, µc = 1.6444.
8. A small-angled prism (µ = 1.62) gives a deviation of 4.8°. Find the angle of the prism.
9. The angle of minimum deviation for a prism of angle π π
is .3 6
What is the velocity of light in the material of the
prism? Given: velocity of light in vacuum = 3 × 108 m s −1. 10. Deduce δm for water (µ = 1.333) when the prism of ∠A
= 60° is used. 11. Calculate the dispersive power of crown glass if the
deviations produced for violet, yellow and light are 4.32°, 4.02° and 3.72y respectively.
12. Calculate the angle of dispersion between red and violet colours produced by a flint glass prism of refracting angle of 60°. Given: µv = 1.663 and µr = 1.622.
13. A glass prism whose refractive index is 1.53 and refracting angle is 60° is held in a liquid of refractive index 1.33. Calculate the angle of minimum deviation in this case.
14. Calculate the dispersive power for crown and flint glass from the following data: C D F Crown 1.5145 1.5170 1.5230 Flint 1.6444 1.6520 1.6637
15. A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. By rotating the prism, the minimum angle of deviation is measured to be 40°. What is the refractive index of the prism? If the prism is placed in water (refractive index 1.33), predict the new minimum angle of deviation of a parallel beam of light. The refracting angle of the prism is 60°.
Topics for Worksheet – IV
Refraction on a curved surface, Lens
Worksheet – IV
1. A beam of light travelling in air strikes a glass sphere of 20 cm diameter converting towards a point 40 cm behind the pole of the spherical surface. Find the position of the image, if the refractive index of glass is 1.5.
2. The image obtained with a convex les in erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object distance and the image distance.
3. The image of a needle placed 45 cm from a lens is formed on a screen placed 90 cm on the other side of lens. Find the displacement of image if the needle is moved 5 cm away from lens.
4. Where should an object be placed from a converging lens of focal length 20 cm so to obtain a real image of magnification 2?
5. An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the image produced by the lens. What happens if the object is moved farther from the lens?
6. A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12 cm front P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?
7. The radius of curvature of each face of a bi-concave lens, made of glass of refractive index 1.5 is 30 cm. Calculate the focal length of the lens in air.
8. Double convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length of the lens is to be 20 cm?
9. A convex lens of focal length f and refractive index 1.5 is immersed in a liquid of refractive index (i) 1.6 (ii 1.3 (iii) 1.5. What is the new focal length in each case?
10. (i) If f = + 0.5 m, what is the power of the lens? (ii) The radii of curvature of the faces of a double
convex lens are 10 cm and 15 cm. Its focal length is 12 cm. What is the refractive index of glass?
(iii) A convex lens has 20 cm focal length in air. What is the focal length in water? (Refractive index for air-water = 1.33, Refractive index for air-glass = 1.5.)
11. Two thin converting lenses of focal lengths 0.15 m and held in contact with each other. Calculate power and focal length of combination.
12. What curvature must be given to the bounding surface of a refracting medium (µ = 1.5) for the virtual image of an object in the adjacent medium (µ = 1) at 10 cm to be formed at a distance of 40 cm?
13. An empty spherical flask of diameter flask of diameter
30 cm is placed in water of refractive index 4
.3
A parallel
beam of light strikes the flask. Where does it get focused, when observed from within the flask.
14. The image of a needle placed 10 cm from a lens is formed on a wall 20 cm on the other side of the lens.
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Find the focal length of lens and size of image formed if the size of object needle is 2.5 cm.
15. A convex lens is to be used to throw on a screen 20 cm from the lens, a magnified image of an object. If the magnification is to be 19, find the focal length of the lens.
16. A needle placed 45 cm from a lens forms an image on a screen placed 90 cm on the other side of the lens. Identify the type of lens and determine its focal length. What is the size of the image if the size of the needle is 5.0 cm?
17. A converting beam of light passes through a diverting lens of focal length 0.2 m and comes to focus 0.3 m behind the lens. Find the position of the point at which the beam would converge in the absence of the lens.
18. The radius of curvature of each surface of a convex lens of refractive index 1.5 is 0.40 m. Calculate its power.
19. An equiconvex lens of focal length 15 cm is cut into two equal halves in thickness. What is the focal length of each half?
20. A glass has a focal length of 5 cm in air. What will be its focal length in water? Refractive index of glass is 1.51 and that of water is 1.33.
21. A glass convex lens has a focal length of 20 cm in air. What will be its focal length, when it is completely immersed in a liquid of refractive index 1.63? Given aµg = 1.5.
22. (a) A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.
(b) Suppose the object in (a) above is in illuminated slit in a collimator tube so that it is hard to measure slit size and its distance from the screen. Using a convex lens, one obtains a sharp image of the slit on a screen. The image size is measured to be 4.6 cm. The lens is displaced away from the slit and at a certain location, another sharp image of size 1.7 cm is obtained. Determine the size of the slit.
Topics for Worksheet – V
Optical instruments
Worksheet – V
1. Far point of a short-sighted person is 100 cm. What lens should he use to see distance objects clearly?
2. A short-sighted person can only see objects distinctly if they lie between 8 cm and 100 cm from the eye. What kind of lens should be required to see a star clearly and what would be its focal length? With these glasses, what would be the least distance of distinct vision?
3. A figure divided into squares, each of size 1 mm2, is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 10 cm) held close to the eye. (i) What is the magnification (image size/object size) produced by the lens ? How much is the area of each square in the virtual image? (ii) What is the angular magnification (magnifying power) of the lens? (iii) Is the magnification in (i) equal to the magnifying power in (ii)? Explain.
4. A person with a normal near point (25 cm) using a compound microscope with and objective of focal length 8.0 mm and eyepiece of focal length 2.5 cm can bring an object placed 9.0 mm from the objective in sharp focus. What is the separation between the two lenses? How much is the magnifying power of the microscope?
12. Two convex lenses of focal lengths 10 cm and 1 cm constitute a telescope. The telescope is focused on a scale which 1 m away from the objective. Calculate the magnification produced and the length of the tube if the final image is formed at a distance of 25 cm from the eye.
13. (a) A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
(b) If this telescope is used to view the Moon, what is the diameter of the image of the Moon formed by the objective lens? The diameter of the Moon is 3.48 × 106 m and the radius of lunar orbit is 3.8 × 108 m.
14. (a) The image of the objective in the eyepiece is known as the ‘eye-ring’. Why is this the best position of our eyes for viewing?
(b) Show that the angular magnification of a telescope equals the ratio of the diameter of objective to the diameter of eye-ring.
(c) The angular magnification of a telescope is 300. What should be the diameter of the objective is our eyes (located at the eye-ring) are just able to collect all the light refracted by the objective? Take the diameter of the pupil of the eye to be 3 mm.
5. A person can see clearly only upto 3 metre. Prescribe a lens for his spectacles so that he can see clearly upto 12 metre.
6. A short-sighted person can see objects most distinctly at a distance of 16 cm. If he wears spectacles at a distance of 1 cm from the eye, what focal length should they have so as to enable him to see distinctly at a distance of 26 cm?
7. To print a photograph from a negative, the time of exposure to light from a lamp placed 0.50 m away is 2.5 second. How much exposure time is required if the lamp is placed 1.0 m away?
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8. A convex lens of focal length 6.25 cm is used as a magnifying glass. If the near point of the observer is 25 cm from the eye and the lens is held close to the eye, calculate (i) the distance of the object from the lens and (ii) the angular magnification.
9. In the previous question, what should be the distance between the object ant the magnifying glass if the virtual image of each square in the figure is to have an area of 6.25 mm2. Would you be to see the squares distinctly with your eyes very close to the magnifier?
10. An angular magnification (magnifying power) of 30 × is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm in a compound microscope. What is the separation between objective and the eyepiece?
11. An amateur astronomer wishes to estimate roughly the size of the Sun using his crude telescope consisting of an objective lens of focal length 200 cm and an eyepiece of focal length 10 cm. By adjusting the distance of the eyepiece from the objective, he obtains an image of the Sun on the screen 40 cm behind the eyepiece. The diameter of the Sun’s image is measured to be 6.0 cm. What is his estimate of the Sun’s size, given that the average Earth-Sun distance is 1.5 × 1011 m?
12. A small telescope has an objective lens of focal length 140 cm and an eyepiece of focal length 5.0 cm. What is magnifying power of the telescope for viewing distance objects when (a) the telescope is in normal adjacent (i.e., when the final image is at infinity), (b) the final image is formed at the least distance of distinct vision (25 cm). (c) What is the separation between the objective and eye-lens in case (a) ? (d) If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens? (e) What is the height of the final image of the tower if it is formed at 25 cm?
CURRICULUM BASED CHAPTER ASSIGNMENT
1 Mark Questions
1. Radius of the curvature of convex mirror 40 cm and the size of the object is twice as that of the image. Then, what is the image distance?
2. When a mirror is rotated through an angle θ, what is the angle turned by the reflected ray?.
3. A concave mirror of focal length f produced an image n size of the object. If the image is real, what is the distance from the mirror?
4. The angle between incident ray and the reflect ray is 70°. What if the angle of incidence?
5. A 5 cm tall object is placed 10 cm from a concave mirror of focal length 15 cm. Find the position, nature and the size of the image.
6. A tall man of height 6 feet want to see his image. Find the required minimum length of the mirror to see his image.
7. Where should an object be placed in front of concave mirror focal length f so that the image to be the same size as the object?
8. What is the magnification produced a plane mirror? 9. If the power of a lens is +5 dioptres, what is the focal
length? 10. A parallel beam of light is incident on a concave lens of
large aperture, Will the reflected coverage at point? 11. Which of the two main parts of an optical fiber has a
higher value of refractive index? 12. A thin prism of 60° angle gives a deviation of 30°. What
is the refractive index of material of prism? 13. What is the refractive index of air for light waves? 14. Mention two conditions of total internal reflection? 15. What happens when white light passes through a
prism? 16. What is a prism? 17. Show the refraction of light by a prism with a suitable
diagram. 18. Give two characteristic properties when the prism is in
the position of minimum deviation? 19. Which of the following colours suffers maximum
deviation in a prism? 20. What is the importance of linear magnification? 21. Where should an object placed in image of the same by
a convex lens? Can it happen in case of a concave lens?
22. How will you judge whether a given piece of glass is convex lens, concave lens or a plane glass sheet?
23. A lens whose radii of curvature are different is forming an image. If the lens is reversed, will the position of image change?
24. What is the nature of the image formed by a concave mirror when the object is placed between its pole and focus?
25. Focal length of an equiconvex lens is equal to the radius of curvature of either face. What is the refractive index of lens material?
26. What should be the position of an object relative to a biconvex lens so that it behaves like a magnifying lens?
27. A converging and a diverging lens of equal focal lengths are place coaxially in contact. Find the power and focal length of the combination.
28. When a biconvex lens made of glass (µ = 1.5) is immersed in water (µ = 1.33), what will happen to its focal length?
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2 Marks Que stions
29. What happen when a monochromic ray passes through a prism?
30. State the law of reflection. 31. What do you mean by the spherical aberration of a
lens? How can it be minimized? 32. Define linear magnification? 33. Mention the use of plane, concave and the convex
mirror. 34. An object is placed between the focus and the pole of a
concave mirror. Locate the position of the image by the ray diagram.
35. What is mean by the linear magnification? 36. Give new Cartesian sigh convention for the spherical
mirrors. 37. A ray of light incident on one face of an equilateral
prism undergoes total internal reflection at another face. If the refractive index of prism material is 2 then, find the angle of incidence (r2) at another face is
38. A ray is incident at an angle of incidence i on one surface of a prism of small angle A and emerges normally from the opposite face. If the refractive index of the prism material is µ, then what angle of incidence?
39. If the angle of a prism is 60° and angle of minimum deviation is 40°. Then find the angle of refraction.
40. Refractive index of glass for light of yellow, green and red colours are µy, µg and µr respectively. Rearrange these symbols in an increasing order of values?
41. At what angle of incidence should a light beam strike a glass slab of refractive-index 3 , such that the reflected and the refracted rays are perpendicular to each other?
42. Show with the help of a diagram the deviation produced by a prism.
43. Define a monochromatic and polychromatic light. How can one obtain monochromatic light from polychromatic light?
44. How deep will a 4 m deep tank appear when seen in air due to optical illusion? Refractive index of water is 4/3.
45. What is dispersion? 46. A concave lens of f = 15 cm forms an image 10 cm from
the lens. Prove that the object is placed 30 cm away from the lens.
47. An object is placed 10 cm in front of a lens. The lens forms a real image three times magnified. Where is the image formed? What is the focal length of the lens?
48. The radius of curvature of either face of a convex lens is equal to its focal length. What is the refractive index of the material of the lens?
49. Calculate the focal length of the combination of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm. Is the system a converging or a diverging lens?
50. A compound microscope with an objective of 1.0 cm focal length and an eye-piece of 2.0 cm focal length has a tude length of 20 cm. calculate the magnifying power of the microscope, if the final image is formed at the neat of the eye.
51. An astronomical telescope, in normal adjustment position has magnifying power 5. The distance between the objective and the eye-piece is 120 cm. calculate the focal lengths of the objective and of the eye-piece.
52. A convex lens of refractive index n1 is held in a medium of refractive index n2 . trace the path of refracted rays of parallel beam of light incident on the lens when (i) n2>n1 and (ii) n2=n1.
53. Using the lens formula, show that a concave lens produces a virtual and diminished image independent of the location of object.
3 Marks Questions
54. An object is placed 10 cm in front of a concave mirror of focal length 15 cm. Find the nature, position and size of the image.
55. An erect image three times the size of the object is obtained with the concave mirror of radius of curvature 36 cm. What is the position of the object?
56. Light of wavelength 5000 0A fall on a reflection surface.
What are the wave length and frequency of reflected ray normal the incident ray?
57. What type mirror will you prefer for the saving or make –up?
58. For dividing a car, which type of mirror would you prefer to see the traffic at your back?
59. What is the difference between virtual image formed by the plane, concave and convex mirror?
60. Described a simple method of finding the focal length of a concave mirror.
61. What are spherical aberration? 62. What do you understand by diffuse reflection? 63. Draw three important rays for a concave mirror that are
generally used to locate the position of the image of an object?
64. Define the dispersive power of a prism. 65. Why does the sky appear blue? 66. A ray of light falls normally on the face of a prism of
refractive index 1.5. Find the angle of the prism if the ray just fails to emerge from the second face.
67. The minimum deviation produced by a glass prism having an angle of 60° is 30°. If the velocity of light in air is 3 × 108 ms–1, calculate its velocity its velocity in glass.
68. A glass prism has a refracting angle of 60°. The angle of minimum deviation is 40°. Find the refractive index.
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At what angle the ray of light should be incident so as to suffer minimum deviation?
69. A ray of light enters a rectangular glass slab of refractive index 3 at an angle of incidence 60°. It travels a distance 5 cm inside the slab and emerges out of the slab. What is the perpendicular distance between the incident and emergent rays?
70. Prove that the refractive index of denser medium w.r.t. rarer medium is equal to the reciprocal of the refractive index of rarer medium w.r.t. denser medium.
71. An object is immersed in water, show that a
w
RealdepthApparent depth
µ =
72. Describe two applications of atmospheric refraction. 73. A myopic person has been using spectacles of power—
1.0 dioptre for distant vision. During old are he also needs to use separate reading glass of power +2.0 dioptre. Explain what may have happened.
74. A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at point O and PO = OQ. Find the distance of the object from the spherical surface.
75. A small point object is placed in air at a distance of 60 cm from the convex spherical refracting surface of refractive index 1.5. If the radius of the curvature of the spherical surface is 25 cm, find the position of the image and power of the refracting surface.
76. An ink dot marked on the surface of glass sphere placed in air is viewed Fig
through the glass from a position directly opposite. If the diameter of the sphere is 15 cm and the refractive index of glass is 1.5, find the position of the image.
77. A convex refracting surface of radius of curvature 15 cm separates two media of refractive indices 4/3 and 1.5. An object is kept in the first medium at a distance of 240 cm from the refracting surface. Calculate the position of the image.
78. A real image of an object id formed at a distance 20cm from a lens. On putting another lens in contact with it, the image is shifted 10 cm toward the combination. Determine the power of the second lens.
79. How does the focal length of a convex lens change if monochromatic red light is used instead of monochromatic blue light?
80. Draw a ray diagram of an astronomical telescope in the normal adjustment position. Write down the expression for its magnifying power.
81. Draw a ray diagram of an astronomical telescope in the near adjustment position. Write down the expression for its magnifying power.
82. Explain why does a convex lens behave as a converging lens when immersed in water (µ = 1.33) and as a diverging lens, when immersed in carbon disulphide (µ = 1.6).
5 Marks Questions
83. Obtain the relation between radius of curvature (R) and the focal length (f) of a convex mirror?
84. A 2.0 cm tall is placed 15 cm from a concave mirror of focal length 10 cm. Find the position, size and nature of the image?
85. Two planes are mirror are inclined to each at angleθ. A ray of light is reflected first at one mirror and mirror then at the other. Fined the total deviation of the ray and show that it is independent of the angle of the incidence at first t mirror.
86. A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length is on the axis of the mirror with the two sides normal to the axis.
87. Two objects A and B when the placed in front of the concave mirror of focal length 7.5 cm give the image of equal size If A is three times the size from the mirror of B and is place 30cm, Find the distance of the object from the pole of the mirror,
88. The angle of minimum deviation for yellow light in a prism of refractive index 1.6 is found to be 46°. Calculate the refracting angle of the prism.
89. In a spectrometer, for the prism A = 60°, calculate the angle of minimum deviation if µ of the prism for orange light is 1.64?
90. Define critical angle, obtain a relation for it. Define total internal reflection. State essential conditions for its occurance.
91. A ray of light is incident at an angle of 60° on one face of a prism which has an angle of 30°. The ray emerging
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out of the prism makes an angle of 30° with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of the prism.
92. A ray of monochromatic light is incident on the refracting face of a prism of refracting angle 75°. It passes through the prism and is incident on the other face at the critical angle. If the refraction index of the prism is 2 , find the angle of incidence on the first face of the prism.
93. A glass prism of angle 72° and refractive index 1.66 is immersed in a liquid of refractive index 1.33.Find the angle of minimum deviation for a parallel beam of light passing through the prism.
94. An object is placed 20 cm to the left of a convex lens of focal length 10 cm. If a concave mirror of focal length 5 cm is placed 30 cm to right of the lens, what is the position of the final image?
95. A diverging lens of focal length 20 cm is placed 60 cm from a pin and a concave mirror of radius of curvature 20cm is placed on the opposite side of the lens. Where should the mirror be placed so that image of the pin may coincide with the pin itself?
96. With the help of the data shown in the ray diagram in fig, calculate the focal length of the concave lens.
QUESTION BANK FOR COMPETITIONS
1. A ray is reflected in turn be three plane mirrors mutually at right angles to each other. The angle between the incident and the reflected rays is: (a) 90° (b) 60° (c) 180° (d) None of these
2. A plane mirror is in front of you in which you can see your image. It is approaching towards you at a speed of 10 cm/s’ then at what speed will your image approach you? (a) 10 cm/s (b) 5 cm/s (c) 20 cm/s (d) 15 cm/s
3. The size of the image, if an object of 2.5 m height is placed at a distance of 10 cm from a concave mirror is: (a) 10.5 m (b) 9.2 m (c) 7.5 m (d) 5.6 m
4. Ray optics fails when the size of the obstacle is: (a) 5 cm (b) 3 cm (c) Less than the wavelength of light (d) (a) and (b) both.
5. Arrange the following in ascending order of frequency. (a) Red, Blue, yellow, green (b) Blue, green ,yellow ,red (c) Red, yellow, green, blue (d) Red, green, yellow, blue
6. One can not see through fog because: (a) Fog absorbs light (b) Light is scattered by the droplets in fog (c) Light surface total internal reflection by the droplets
in fog (d) The refractive index of fog is infinity
7. The refractive index of the medium if a light wave has a frequency of 4 × 1014 Hz and a wavelength of 5 × 10–7 m in a medium, will be: (a) 1.5 (b) 1.33 (c) 1.0 (d) 0.66
8. The number of wavelengths in the visible spectrum is: (a) 4000 (b) 6000 (c) 2000 (d) Infinite
9. Find the length of the optical path of two media in contact of lengths d1 and d2 of refractive indices µ1 and µ2 respectively. (a) µ1 d1 + µ2d2 (b) µ1 d2 + µ2d1
(b) 1 2
1 2
d dµ µ
(d) 1 2
1 2
d d+µ µ
10. Calculate the refractive index of glass with respect to water. It is given that refractive indices of glass and
water with respect to air are 3 3
and2 4
respectively:
(a) 89
(b) 98
(c) 76
(d) None of these
11. When a prism is dipped in water then the angle of minimum deviation of a prism with respect to air will be:
a g a w
3 4,
2 3 µ = µ =
(a) 18
(b) 12
(c) 34
(d) 14
12. An astronomical telescope has a large aperture to: (a) Reduce spherical aberration (b) Have high resolution (c) Increase span of observation (d) Have low dispersion
13. To get three images of a single object, one should have two plane mirrors at an angle of: (a) 60º (b) 90º (c) 120º (d) 30º
14. A thin glass (refractive index 1.5) lens has optical power of – 5D in air. Its optical power in a liquid medium with refractive index 1.6 will be: (a) 1D (b) –1D (c) 25D (d) –25D
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15. A plane mirror. (i) Can form real object (ii) Neither converges nor diverges the rays (iii) Cannot form real image of a real object.
Choose the correct option or options. (a) (i) is correct (b) (i) and (ii) are correct (c) (ii) and (iii) are correct (d) None of all above
16. A man of height 1.8 m stands in front of large vertical plane mirror. The distance of the image from the main if he stands at a dis tance of 1.5 m from the mirror is: (a) 1 m (b) 2 m (c) 3 m (d) 4 m
17. A man is running towards a plane mirror with some velocity. If the relative velocity of his image with respect to him is 4 m/s, then the velocity of a man is: (a) 2 m/s (b) 4 m/s (c) 15 m/s (d) 16 m/s
18. The mirrors are perpendicular to each other as shown in figure. A light ray a light ray AB is incident on the mirror M1. Then the reflected ray wills also surfer a reflection from the mirror M2. Then the final ray after reflection from M2 will be parallel to the incident ray, if:
i
B
M2
M1
(a) I =45° (b) I = 65° (c) I < 30° (d) for any I between 0° and 90°
19. A pole 5 m high on a horizontal surface. Sun rays rare incident at an angle 30° with vertical. The size or shadow on horizontal surface is: (a) 5 m
(b) 5
m3
(c) 10
m3
(d) None of these
20. A point object P is situated in front of plane mirror shown in figure. The width of mirror AB is d. The visual region on a line passing through point P and parallel to the mirror is:
d
A
B
45°
P
(a) d (b) 2d (c) 3d (d) None of the above
21. A beautiful girl with two normal eyes wants to see full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face are 4 inch and 6 inch respectively. The minimum width of the required mirror is: (a) 1 inch (b) 2 inch (c) 3 inch (d) 4 inch
22. A ray f light falls on a plane mirror. When th e mirror is turned, about an axis at right angle to the plane of the mirror through 20°, the angle between the incident ray and new reflected ray is 45°.The angle between the incident ray and original reflected ray is: (a) 15° (b) 30° (c) 45° (d) 60°
23. A lamp and scale arrangement, used to measure small deflected is shown in the figure. SS’ is the glass scale placed at a distance of 1 MM and I is the position of the light spot formed after reflection from the under deflected mirror MM. the mirror is deflected by 10° and comes to the deflected position MM. the distance moved by the spot on the scale is:
M’
M
R
S
I1 m
10°
M’
M
S
(a) 24.6 cm (b) 36.4 cm (c) 46.4 cm (d) 34.9 cm
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24. A plane mirror, reflecting a ray of incident light, is rotated through an angle θ about an axis through the point of incidence in the plane of the mirror perpendicular of the plane of incidence, then: (a) The reflected ray does not rotated (b) The reflected ray rotates through an angle θ (c) The reflected ray rotates through an angle θ (d) The incident ray is fixed
25. In the given figure, the angle between reflected rays is equal to:
A
(a) A (b) 2A (c) 3A (d) 4A
26. A vessel consists of two plane mirrors at right angles (as shown in figure). The vessel is filled with water. The total deviation in incident ray is:
90°
(a) 0° (b) 90° (c) 180° (d) None of the above
27. Two plane mirrors are placed parallel to each other as shown in the figure. There is an object O placed between the mirrors, at 5 cm from mirror M2. What are the distances of first three images from M2?
O
15 cm
M1 M2
(a) 5,10,15 (b) 5,15,30 (c) 5, 25, 25 (d) 5,15,25
28. If two mirrors are inclined at some angle and an object is placed between the mirrors and there are 7 images formed for an object, then what is angle between the mirrors? (a) 54° (b) 50° (c) 60° (d) 45°
29. If u represents object distance from pole of spherical mirror and v represents image distance from pole of mirror and f is the focal length of the mirror, then a straight line u = v measurement of f is: (a) (f,f) (b) (2f,2f) (c) (f, 2f) (d) (0,0)
30. The position of 1 cm tall object which speed is placed 8 cm in front of a concave mirror of radius of curvature 24 cm is: (a) 24 cm (b) 25 cm (c) 26 cm (d) 27 cm