Optical Instruments

Chapter 25

Introduction

We will discuss: Cameras The eye The simple magnifier The compound microscope The telescope The Michelson interferometer The diffraction grating

The Camera

A single lens camera consists of: A light tight box A converging lens

Produces a real, inverted imageFocusing is done by adjusting the distance between

the lens and the film. A shutter

25.1

Camera Variables

Shutter speeds Control exposure times Faster shutter speeds for faster objects or

for bright light Aperture size

Larger aperture needed for low light conditions

f-number The ratio of the focal length to the diameter of the

lens

Determines the speed of the lens A measure of the light concentrating power of the

lens A small f-number means that the aperture is wide

open€

f - number =f

D

The equation for lateral magnification:

p

q

h

hM

'

−==

The London Eye

The Human Eye

Parts of the eye: Cornea Aqueous humor Iris and pupil Crystalline lens Vitreous humor Retina

Rods and conesB13

Accommodation Ciliary muscles

Relaxed when viewing distant objects

The focal length of the eye is about 1.7 cm.

The cornea does over 70 % of the refracting.

The lens makes the final adjustment.

The Near Point

The near point is the closest distance for which the lens will produce a sharp image of a nearby object on the retina. About 18 cm at age 10 About 25 cm at age 20 About 50 cm at age 40 500 cm or greater at age 60

The Far Point

The far point is the farthest distance for which the lens will produce a sharp image of a far away object on the retina. Objects located beyond the far point will

be out of focus.

Defects of the Eye

Hyperopia (farsightedness) Corrected with a converging lens

Myopia (nearsightedness) Corrected with a diverging lens

Astigmatism Corrected by using cylindrical lenses

25.3, 25.4, 30-1

Astigmatism Test

Diseases of the Eye

Cataracts The lens is surgically

replaced

Glaucoma Corrected by medication or YAG solid

state laser surgery

The Power (P) of a Lens

Measured in diopters (no abbreviation) Used in lens prescriptions

Formula:

f must be in meters

f

1P =

The Simple Magnifier

Consists of a single converging lens Increases the apparent size of an object

25.6a, b

Angular Magnification (m)

Angular Magnification is the ratio of the angle subtended by the object when the lens is in use to the angle subtended by the object when it is placed at the near point with no lens

€

m =θ

θo

Maximum angular magnification occurs when the image formed by the lens is at the near point of the eye (more eye stress).

f

25cm1m +=

Angular magnification (m) when the image formed by the lens is at infinity (relaxed eye):

f

25cmm =

The Compound Microscope

Uses two lenses to achieve greater magnification than the simple magnifier An objective with a short focal length ( ) An eyepiece (ocular) with a focal length ( ) of a few centimeters Lenses are separated by a distance (L)

which is greater than either or25.7a

of

ef

of ef

Microscope Images

The image formed by the objective becomes the object for the eyepiece.

The image is inverted with respect to the object.

Microscope Equations

Magnification equations:

)cm 25

(L

mMM 1eo

e ff−==

o1 f

LM −=

€

me =25cm

fe

The Electron Microscope

Atoms could never be seen with a compound microscope by using visible light The wavelength of light is too large

The Telescope

There are two fundamentally different types of telescopes.

The Refracting Telescope

The Reflecting Telescope

The Refracting Telescope

It uses a combination of lenses. The image (q1) formed by the first lens becomes the

object (p2) for the second lens.

The image is inverted.

25.8a e

o

f

f−=meo ff +=L

Refracting Telescope Difficulties

Large refracting telescopes are difficult to manufacture and are expensive.

In addition, their large masses would lead to sagging which would cause distortion.

The Reflecting Telescope

Reflecting telescopes are preferred in astronomy. A parabolic mirror replaces the objective.

Spherical aberration is reduced.Chromatic aberration is

virtually eliminated.

The Newtonian Focus

Reflecting Telescopes use the Newtonian focus.

Large Telescopes

The largest telescopes in the world are reflecting telescopes. 10 meter lens in Hawaii 5 meter lens on Mt. Palomar in California

Canada-France-Hawaii

Mt. Palomar

The largest refracting telescope in the world is at Yerkes Observatory in Wisconsin Only 1 meter in diameter

Yerkes Observatory

Images

Microscopes and telescopes can only form virtual images.

Resolution Of Single-Slit And Circular Apertures

It is important to be able to distinguish between two closely spaced objects. This ability is limited by the diffraction of

light

25.10

Maximum Resolution

If the two sources are separated so that their central maxima do not overlap, their images can be distinguished and they are said to be resolved. Maximum resolution occurs at the shortest

possible wavelength.

265

Rayleigh’s Criterion

When the central maximum of one image falls on the first minimum of another image, the images are said to be resolved.

Equations for the resolution of a circular aperture ( is in radians)

266

€

min = 1.22λ

D

€

= s

r

The Diffraction Grating

Diffraction gratings are preferred over single or double slits when accurate wavelength measurements are needed. They have a much higher resolution and provide a

brighter pattern.

€

sinθ = mλ

d

€

sinθ = y

L

The Michelson Interferometer

It splits a light beaminto two parts and then recombines them toform an interferencepattern.

262

The Michelson Equation

L is the length of travel of the adjustable mirror.N is the number of fringe shifts.

€

ΔL = Nλ

4

⎛

⎝ ⎜

⎞

⎠ ⎟

Questions

1, 3, 4, 6 - 9, 11, 13

Pg. 842