Topic: GEOMETRICAL OPTICS 1. A reflecting surface is represented by the equation Y= 2L x sin L π π , 0 ≤ x ≤ L. A ray travelling horizontally becomes vertical after reflection. The coordinates of the point(s) where this ray is incident is (A) L 2L , 4 π (B) L 3L , 3 π (C) 3L 2L , 4 π (D) 2L 3L , 3 π 2. A cubical block of glass of refractive index n 1 is in contact with the surface of water of refractive index n 2 . A beam of light is incident on vertical face of the block (see figure). After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle θ . The value of θ is given by : (A) sin θ < 2 2 1 2 n n - (B) tan θ < 2 2 1 2 n n - (C) sin θ < 2 2 1 2 1 n n - (D) tan θ < 2 2 1 2 1 n n - 3. A beam of diameter ‘d’ is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be: (A) 3 4 d (B) d (C) d 3 (D) 2 3 d 4. A glass sphere of index 1.5 and radius 40 cm has half its hemispherical surface silvered. The point where a parallel beam of light, coming along a diameter, will focus (or appear to) after coming out of sphere, will be:
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Topic: GEOMETRICAL OPTICS
1. A reflecting surface is represented by the equation Y=2L x
sinL
π π
, 0≤ x ≤ L. A ray travelling horizontally
becomes vertical after reflection. The coordinates of the point(s) where this ray is incident is
(A) L 2 L
,4
π
(B) L 3 L
,3
π
(C) 3L 2 L
,4
π
(D) 2L 3 L
,3
π
2. A cubical block of glass of refractive index n1 is in contact with the surface of water of refractive index n2. A
beam of light is incident on vertical face of the block (see figure). After refraction, a total internal reflection at the
base and refraction at the opposite vertical face, the ray emerges out at an angle θ . The value ofθ is given by :
(A) sinθ < 2 2
1 2n n− (B) tanθ < 2 2
1 2n n−
(C) sinθ <2 2
1 2
1
n n− (D) tanθ <
2 2
1 2
1
n n−
3. A beam of diameter ‘d’ is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is
very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be:
(A) 3
4d (B) d (C)
d
3 (D)
2
3d
4. A glass sphere of index 1.5 and radius 40 cm has half its hemispherical surface silvered. The point where a
parallel beam of light, coming along a diameter, will focus (or appear to) after coming out of sphere, will be:
(A) 10 cm to the left of centre (B) 30 cm to the left of centre
(C) 50 cm to the left of centre (D) 60 cm to the left of centre
Question No. 5 to 8(4 questions)
The figure shows a transparent sphere of radius R and refractive indexµ . An object O is placed at a distance x
from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface.
5. If x = 2R, then the value of µ is
(A) 1.5 (B) 2 (C) 3 (D) none of these
6. If x =∞ , then the value of µ is
(A) 1.5 (B) 2 (C) 3 (D) none of these
7. If an object is placed at a distance R from the pole of first surface, then the real image is formed at a distance R
from the pole of the second surface. The refractive index µ of the sphere is given by
(A) 1.5 (B) 2 (C) (D) none of these
8. In previous problem, if the refractive index of the sphere is varied, then the position x of the object and its image
from the respective poles will also vary. Identify the correct statement.
(A) If the value of µ increases the value of x decreases
(B) If the value of µ becomes equal to unity, then x tends to infinity
(C) The value of µ must not be less than 1
(D) All the above
9. A point objects O moves from the principal axis of a converging lens in a direction OP. I is the
image of O, will move initially in the direction
(A) IQ (B) IR (C) IS (D) IU
10. A thin symmetric double - convex lens of power P is cut into three parts A, B and C as shown.
The power of
(A) A is P (B) A is 2P (C) B is P (D) B is P/4
11. When the object is at distances u1 and u2 the images formed by the same lens are real and virtual respectively and
of the same size. Then focal length of the lens is:
(A) 1 2
1u u
2 (B)
1 2
1(u u )
2+ (C) 1 2u u (D) 2 (u1 + u2)
12. Two planoconvex lenses each of focal length 10 cm & refractive index 3/2 are placed as shown. In the space left,
water (R.I = 4/3) is filled. The whole arrangement is in air. The optical power of the system is (in diopters):
(A) 6.67 (B) – 6.67 (C) 33.3 (D) 20
13. A concave mirror is placed on a horizontal surface and two thin uniform layers of different transparent liquids
(which do not mix or interact) are formed on the reflecting surface. The refractive indices of the upper and lower
liquids are µ 1 and µ 2 respectively. The bright point source at a height‘d’ (d is very large in comparison to the
thickness of the film) above the mirror coincides with its own final image. The radius of curvature of the
reflecting surface therefore is
(A) 1
2
dµµ
(B) µ 1µ 2d (C) µ 1d (D) µ 2d
14. If an object is placed at A (OA>f); Where f is the focal length of the lens the image is found to be formed at B. A
perpendicular is erected at o and C is chosen on it such that the angle ∠ BCA is a right angle. Then the value of f