Chapter 25 Optical Instruments Conceptual questions: 3,6,7,8,9 Quick quiz: 2 Problem: 10,26,48.

Chapter 25Chapter 25Optical InstrumentsOptical Instruments

Conceptual questions: 3,6,7,8,9

Quick quiz: 2

Problem: 10,26,48

The The CameraCamera The ƒ-number of a The ƒ-number of a

camera is the ratio of camera is the ratio of the focal length of the the focal length of the lens to its diameterlens to its diameter

ƒ = f/Dƒ = f/D

The ƒ-number is often The ƒ-number is often given as a description of given as a description of the lens “speed”the lens “speed”

The lowest ƒ-number The lowest ƒ-number setting on a camera setting on a camera corresponds to the corresponds to the aperture wide open and aperture wide open and the maximum possible the maximum possible lens area in uselens area in use

M=h’/h=-q/p

h’=-hf/p

Camera with small f produces small images

The EyeThe Eye

Essential parts of the Essential parts of the eyeeye Cornea – light passes Cornea – light passes

through this through this transparent structuretransparent structure

Aqueous Humor – clear Aqueous Humor – clear liquid behind the cornealiquid behind the cornea

The pupilThe pupil A variable aperture A variable aperture An opening in the irisAn opening in the iris

The crystalline lensThe crystalline lens The retinaThe retina

The retina contains The retina contains receptors called rods and receptors called rods and conescones

IrisIris

The iris is the colored portion of the The iris is the colored portion of the eyeeye It is a muscular diaphragm that It is a muscular diaphragm that

controls pupil sizecontrols pupil size The iris regulates the amount of light The iris regulates the amount of light

entering the eye by dilating the pupil entering the eye by dilating the pupil in low light conditions and contracting in low light conditions and contracting the pupil in high-light conditionsthe pupil in high-light conditions

The f-number of the eye is from about The f-number of the eye is from about 2.8 to 162.8 to 16

The Eye – The Eye – OperationOperation

Rods and ConesRods and Cones Chemically adjust their sensitivity according to Chemically adjust their sensitivity according to

the prevailing light conditionsthe prevailing light conditions The adjustment takes about 15 minutesThe adjustment takes about 15 minutes This phenomena is “getting used to the dark”This phenomena is “getting used to the dark”

AccommodationAccommodation The eye focuses on an object by varying the The eye focuses on an object by varying the

shape of the crystalline lens through this processshape of the crystalline lens through this process An important component is the An important component is the ciliary muscleciliary muscle

which is situated in a circle around the rim of the which is situated in a circle around the rim of the lenslens

Thin filaments, called Thin filaments, called zonuleszonules, run from this , run from this muscle to the edge of the lensmuscle to the edge of the lens1/f = 1/p +1/q for an eye q=1.7 cm

The Eye -- FocusingThe Eye -- FocusingLens maker’s formulae

1 2

1 1 1( 1)( )n

f R R

1 1 1

1.7f p cm Lens equation

When the eye focuses on a distant object, the ciliary muscle the ciliary muscle is relaxed and the zonules tighten, as a result is relaxed and the zonules tighten, as a result the lens flattens, R1 and R2 increase.

When the eye focuses on near objects, the ciliary When the eye focuses on near objects, the ciliary muscles tenses, this relaxes the zonules, and the lens muscles tenses, this relaxes the zonules, and the lens bulges a bit and the focal length decreases. The bulges a bit and the focal length decreases. The image is focused on the retina.image is focused on the retina.

The Eye – Near and Far The Eye – Near and Far PointsPoints

The The near pointnear point is the closest distance for is the closest distance for which the lens can accommodate to which the lens can accommodate to focus light on the retinafocus light on the retina Typically at age 10, this is about 18 cmTypically at age 10, this is about 18 cm It increases with ageIt increases with age

The The far pointfar point of the eye represents the of the eye represents the largest distance for which the lens of the largest distance for which the lens of the relaxed eye can focus light on the retinarelaxed eye can focus light on the retina Normal vision has a far point of infinityNormal vision has a far point of infinity

FarsightednessFarsightedness

Also called hyperopiaAlso called hyperopia The image focuses behind the retinaThe image focuses behind the retina Can usually see far away objects Can usually see far away objects

clearly, but not nearby objectsclearly, but not nearby objects

Correcting FarsightednessCorrecting Farsightedness

A converging lens placed in front of the eye can A converging lens placed in front of the eye can correct the conditioncorrect the condition

The lens refracts the incoming rays more toward The lens refracts the incoming rays more toward the principle axis before entering the eyethe principle axis before entering the eye This allows the rays to converge and focus on the retinaThis allows the rays to converge and focus on the retina

NearsightednessNearsightedness

Also called myopiaAlso called myopia In In axial myopiaaxial myopia the nearsightedness is caused the nearsightedness is caused

by the lens being too far from the retinaby the lens being too far from the retina In In refractive myopiarefractive myopia, the lens-cornea system is , the lens-cornea system is

too powerful for the normal length of the eyetoo powerful for the normal length of the eye

Correcting Correcting NearsightednessNearsightedness

A diverging lens can be used to correct A diverging lens can be used to correct the conditionthe condition

The lens refracts the rays away from the The lens refracts the rays away from the principle axis before they enter the eyeprinciple axis before they enter the eye This allows the rays to focus on the retinaThis allows the rays to focus on the retina

DioptersDiopters

The power of a lens in diopters equals The power of a lens in diopters equals the inverse of the focal length in the inverse of the focal length in metersmeters

P = 1/ƒP = 1/ƒ

Problem 10.Problem 10.

A PERSON HAS THE FAR POINT A PERSON HAS THE FAR POINT 84.4 CM FROM THE RIGHT EYE 84.4 CM FROM THE RIGHT EYE AND 122 CM FROM THE LEFT EYE. AND 122 CM FROM THE LEFT EYE. FIND THE POWERS FOR THE FIND THE POWERS FOR THE CORRECTIVE LENSES.CORRECTIVE LENSES.

The Size of a Magnified The Size of a Magnified ImageImage

lenswithoutangle

lenswithanglem

o

Angular magnificationAngular magnification is defined asis defined as

max

251

cmm

f

Magnification by a LensMagnification by a Lens

With a single lens, it is possible to With a single lens, it is possible to achieve angular magnification up achieve angular magnification up to about 4 without serious to about 4 without serious aberrationsaberrations

With multiple lens, magnifications With multiple lens, magnifications of up to about 20 can be achievedof up to about 20 can be achieved The multiple lens can correct for The multiple lens can correct for

aberrationsaberrations

Compound MicroscopeCompound Microscope

The image formed by the The image formed by the first lens becomes the first lens becomes the object for the second lensobject for the second lens

The image seen by the The image seen by the eye, Ieye, I22, is virtual, inverted , is virtual, inverted and very much enlargedand very much enlarged

Magnifications of the Compound Magnifications of the Compound MicroscopeMicroscope

The The lateral magnificationlateral magnification of the objective is of the objective is

– L is the distance between the lensesL is the distance between the lenses

The The angular magnificationangular magnification of the eyepiece of the eyepiece of the microscope isof the microscope is

The The overall magnificationoverall magnification of the of the microscope is the product of the individual microscope is the product of the individual magnificationsmagnifications

ol

ll ƒ

L

p

qM

ee ƒ

cm25m

eoel ƒ

cm25

ƒ

LmMm

TelescopesTelescopes

Two fundamental types of telescopesTwo fundamental types of telescopes Refracting telescope uses a combination of Refracting telescope uses a combination of

lens to form an imagelens to form an image Reflecting telescope uses a curved mirror Reflecting telescope uses a curved mirror

and a lens to form an imageand a lens to form an image Telescopes can be analyzed by Telescopes can be analyzed by

considering them to be two optical considering them to be two optical elements in a rowelements in a row The image of the first element becomes the The image of the first element becomes the

object of the second elementobject of the second element

Refracting TelescopeRefracting Telescope The two lenses are The two lenses are

arranged so that the arranged so that the objective forms a real, objective forms a real, inverted image of a inverted image of a distance objectdistance object

The image is near the The image is near the focal point of the eyepiecefocal point of the eyepiece

The two lenses are The two lenses are separated by the distance separated by the distance ƒ ƒoo + ƒ + ƒee which corresponds which corresponds to the length of the tubeto the length of the tube

The eyepiece forms an The eyepiece forms an enlarged, inverted image enlarged, inverted image of the first imageof the first image

Angular Magnification of a Angular Magnification of a TelescopeTelescope

The angular magnification depends on The angular magnification depends on the focal lengths of the objective and the focal lengths of the objective and eyepieceeyepiece

e

o

o ƒ

ƒm

The limiting angle of resolution depends The limiting angle of resolution depends on the diameter, D, of the apertureon the diameter, D, of the aperture

D22.1min

Reflecting Telescope, Reflecting Telescope, Newtonian FocusNewtonian Focus

The incoming rays The incoming rays are reflected from are reflected from the mirror and the mirror and converge toward converge toward point Apoint A At A, a photographic At A, a photographic

plate or other detector plate or other detector could be placedcould be placed

A small flat mirror, M, A small flat mirror, M, reflects the light reflects the light toward an opening in toward an opening in the side and passes the side and passes into an eyepieceinto an eyepiece

Examples of TelescopesExamples of Telescopes

Reflecting TelescopesReflecting Telescopes Largest in the world are 10 m diameter Largest in the world are 10 m diameter

Keck telescopes on Mauna Kea in HawaiiKeck telescopes on Mauna Kea in Hawaii Largest single mirror in US is 5 m Largest single mirror in US is 5 m

diameter on Mount Palomar in Californiadiameter on Mount Palomar in California Refracting TelescopesRefracting Telescopes

Largest in the world is Yerkes Largest in the world is Yerkes Observatory in WisconsinObservatory in Wisconsin

Has a 1 m diameterHas a 1 m diameter

The diffraction pattern of a circular The diffraction pattern of a circular aperture consists of a central, aperture consists of a central, circular bright region surrounded circular bright region surrounded by progressively fainter ringsby progressively fainter rings

The limiting angle of resolution The limiting angle of resolution depends on the diameter, D, of the depends on the diameter, D, of the apertureaperture

D22.1min

Resolution with Circular Resolution with Circular AperturesApertures

ResolutionResolution

min a

For the images to For the images to be resolved, the be resolved, the angle subtended angle subtended by the two by the two sources at the sources at the slit must greater slit must greater than than θθminmin

Suppose you are observing a binary star with a telescope and are having difficulty resolving the two stars. You decide to use a colored filter to help you. Should you choose a blue filter or a red filter?

QUICK QUIZ 25.2

Michelson InterferometerMichelson Interferometer One ray is reflected to One ray is reflected to

MM11 and the other and the other transmitted to Mtransmitted to M22

After reflecting, the After reflecting, the rays combine to form rays combine to form an interference patternan interference pattern

The glass plate The glass plate ensures both rays ensures both rays travel the same travel the same distance through glassdistance through glass

Measurements with a Measurements with a Michelson InterferometerMichelson Interferometer

The interference pattern for the two rays is The interference pattern for the two rays is determined by the difference in their path lengthsdetermined by the difference in their path lengths

When MWhen M11 is moved a distance of is moved a distance of λ/4, successive λ/4, successive light and dark fringes are formedlight and dark fringes are formed This change in a fringe from light to dark is This change in a fringe from light to dark is

called called fringe shiftfringe shift The wavelength can be measured by counting the The wavelength can be measured by counting the

number of fringe shifts for a measured number of fringe shifts for a measured displacement of Mdisplacement of M

If the wavelength is accurately known, the mirror If the wavelength is accurately known, the mirror displacement can be determined to within a displacement can be determined to within a fraction of the wavelengthfraction of the wavelength

Conceptual questionsConceptual questions 6. 6. Compare and contrast the eye and a camera. Compare and contrast the eye and a camera.

What parts of the camera correspond to the iris, What parts of the camera correspond to the iris, the retina, and the cornea of the eyethe retina, and the cornea of the eye? ?

3. The optic nerve and the brain invert the image 3. The optic nerve and the brain invert the image formed on the retina. Why do we not see formed on the retina. Why do we not see everything upside down?everything upside down?

8. 8. If you want to use a converging lens to set fire If you want to use a converging lens to set fire to a piece of paper, why should the light source be to a piece of paper, why should the light source be farther from the lens than its focal point? farther from the lens than its focal point?

7. Large telescopes are usually reflecting rather 7. Large telescopes are usually reflecting rather than refracting. List some reasons for this choice. than refracting. List some reasons for this choice.

9. Explain why it is theoretically impossible to see 9. Explain why it is theoretically impossible to see an object as small as an atom regardless of the an object as small as an atom regardless of the quality of the light microscope being used. quality of the light microscope being used.

Problem 25.26Problem 25.26

A certain telescope has an objective of focal length 1 500 cm. If the Moon is used as an object, a 1.0 cm long image formed by the objective corresponds to what distance, in miles, on the Moon? Assume 3.8 × 108 m for the Earth–Moon distance.

Problem 25-48Problem 25-48 A person with a nearsighted eye has near and A person with a nearsighted eye has near and

far points offar points of 16 cm and 25 cm, respectively. 16 cm and 25 cm, respectively. (a) Assuming a lens is(a) Assuming a lens is placed 2.0 cm from the placed 2.0 cm from the eye, what power must the lenseye, what power must the lens have to have to correct this condition? (b) Suppose that correct this condition? (b) Suppose that contactcontact lenses placed directly on the cornea lenses placed directly on the cornea are used to correctare used to correct the person’s eye. What is the person’s eye. What is the power of the lens required inthe power of the lens required in this case, this case, and what is the new near point? [and what is the new near point? [Hint:Hint: The The contactcontact lens and the eyeglass lens require lens and the eyeglass lens require slightly differentslightly different powers because they are at powers because they are at different distances from thedifferent distances from the eye.]eye.]