Ch 25 1

Chapter 25

Optical Instruments

© 2006, B.J. LiebSome figures electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey

Giancoli, PHYSICS,6/E © 2004.

Ch 25 2

Camera

•A camera lens must produce a real image on the film. This may require adjusting the lens position (di) to focus it.

•The iris diaphragm controls the area of the lens through which light can pass.

•The shutter opens briefly to expose the film.

Ch 25 3

Digital Cameras

•Charge Coupled Devices (CCD) are rapidly replacing film in cameras.

•Light that passes through a color filter can produce an electron by the photoelectric effect (Chapter 27)

•Total charge stored is read out.

•A color pixel is two greens and a red and a blue.

Ch 25 4

Camera Lens

•Shutter speed: How long the shutter is open

•Focusing: Moves the lens to produce the sharpest image on the film or CCD.

•Diameter of lens = D

•Focal length of lens = f

•The f-stop of a lens is defined as

•The smallest f-stop is referred to as the speed of the lens. (Smaller is better since a large D means more light is admitted.)

D

fstopf

Ch 25 5

Camera Lens

•Normal lens – gives picture with field of view similar to human eye. f = 50 mm.

•Telephoto lens – magnifies image. Typical telephoto has f = 200 mm which magnifies image by factor of ~ 4.

•Wide Angle – field of view larger than human eye. f = 30 mm.

•Zoom lens – focal length is variable. Combines a converging lens with a diverging lens that moves to adjust the focal length of the combination.

Lens moves to focus image on CCD or film. So image distance is adjusted.

Ch 25 6

Human Eye

Optics is similar to a camera:

•Iris (colored part of eye) controls light input

•Pupil is the hole in the iris

•Retina takes place of film- has rods and cones which are sensitive to light

•Cones give fine detail and color

•Rods provide a gray image in low light situations

Ch 25 7

Human Eye

•No shutter but nervous system “sees” about 30 images per second, similar to a video camera

•Cornea does most of the bending of the light rays

•Lens does fine adjustment to focal length to focus image. Unlike the camera, the image distance is fixed.

Ch 25 8

Accommodation

•Accommodation is the adjustment of lens shape to focus the image onto the retina. Muscles pull on lens and change its shape.

•Near Point ( N ) closest distance that the eye can focus clearly. For “normal” eye, near point 25 cm.

•Far Point: farthest point that eye can focus. For “normal” eye, far point is infinity (i.e. parallel rays).

•Nearsightedness: eye that can focus only on nearby objects.

•Farsightedness: eye that cannot focus on nearby objects

•Relaxed Eye: focused on infinity

Ch 25 9

Correcting Eye Defects with Lenses

Ch 25 10

Example 25-1: A person is to be fitted with bifocals. She can see an object clearly when it is between 50 cm and 1.5 m from the eye.

A. The upper portion of the bifocals should enable her to see distant objects clearly. What power should they have?

od

mdi 5.1

fdd

111

io

fm

1

5.1

11

mf 5.1

)diopters(67.01

Df

power

negative because not on side of lens to which light is going.

Ch 25 11

Example 25-1B. The lower portion of the bifocals should enable her to see objects at a distance of 25 cm from the lens. What power should they have?

An object held at the near point, 25 cm, should have an image at 50 cm from the eye so she can focus on it.

cmd 25o

cmd 50i

fdd

111

io

fcmcm

1

50

1

25

1

cmf 50

Dmf

0.250.0

11power

negative because not on side of lens to which light is going.

Ch 25 12

Magnifying Glass

•As an object is moved closer, the image of the object on the retina is larger, so it appears larger to us

•If object is brought closer than the near point, we can not focus it

•A magnifying glass allows us to bring the object closer, while still having the image at the near point.

Ch 25 13

Magnifying glass with eye focused at near point.

•The greatest magnification results if the eye is focused on the near point N (Note di = -N)

Nfdfd io

11111

Nf

Nd

N

Nh

dhM

o

o 11

/

/'

1f

NM Eye focused on near point.

Ch 25 14

Astronomical Refracting Telescope

•The telescope shown above produces an inverted image

•Objective lens forms real image at its focal point (fo)

•Eyepiece ( fee )) acts as a magnifying glass on this image

•Θ h / fo where h is image from objective and tanθ θ

•θ’ h / fe (look at thick ray which is parallel to axis)

•The magnification is: M = θ’ / θ and thus:

• Negative M indicates an inverted image.

e

o

f

fM

Ch 25 15

Astronomical Reflecting Telescope

•Mirror takes place of objective lens in previous telescope but optics is the same

•Drawing shows two ways of getting light “out”

•Mirrors can be made much larger because they can be supported from below.

•Diameter of mirror determines light-gathering ability which is most important in astronomy

Ch 25 16

Example 25-2: (72) An astronomical telescope has a magnification of 8.0. If the two lenses are 28 cm apart, determine the focal length of each lens.

0.8e

o

f

fM

eoff 0.8

cmffeo

28

cmff ee 280.8

cmfe

280.9

cmfe

1.3

cmff eo 250.8

Ch 25 17

Compound Microscope

•Unlike telescope, object is very close

•Objective (fo ) and eyepiece (fe) play similar role as with telescope.

•If l is distance between lenses and N is near point:

oe ff

lNM

Ch 25 18

Example 25-3: A microscope uses an eyepiece with a focal length of 1.5 cm. Using a normal eye with a final image at infinity, the tube length is 17.5 cm and the focal length of the objective lens is 0.65 cm. What is the magnification of the microscope?

)pointnear(25cmN

cmfe

5.1cmf

o65.0

cml 5.17

oe ff

lNM

)65.0)(5.1(

)5.17)(25(

cmcm

cmcmM X450

Ch 25 19

Lens AberrationsSpherical aberration: rays that pass through the outer regions of the lens are brought to a different focal point then those that pass through the center.

Chromatic aberration: different colors are focused at different points. Can be reduced with compound lens. Some camera lenses have 6 to 8 elements.

Ch 25 20

Rayleigh Criterion•Resolution: ability of a lens to produce distinct images of two point objects

•Resolution is limited by

•Various aberrations

•Diffraction

•Rayleigh Criterion: angular limit of resolution of light of wavelength passing through a lens of diameter D. The factor of 1.22 results from treating a circular hole as the average of a slit.

D

22.1

Ch 25 21

Example 25-4: A spy satellite carries out surveillance with a special high-resolution camera with a lens diameter of 40.0 cm that is limited only by diffraction. Estimate the separation of two small objects on the surface of the earth that can be resolved in the light of 500 nm if the satellite is 250 km above the surface of the earth.

D

22.1

)40.0(

)10500)(22.1( 9

cm

m

rad61053.1

θ

rs

)1053.1)(10250( 63 radms rs

ms 38.0

Ch 25 22

X-Ray Diffraction•Useful technique for studying crystals, molecules such as DNA etc.

•X-rays are produced when accelerated electrons strike a glass or metal surface.

•X-rays have smaller than atomic spacing

Conditions for constructive interference between subsequent layers of the crystal separated by distance d.

ri

sindm 2

Note that angle definition is not the same as in optics chapter.

....,, 321m