Chapter 19 Physics: Optical Instruments

Front 1

Thin- Lens Equation

Back 1

Note: the thin lens equation can be used for both mirrors and lenses
Where f is the focal length, s is the object distance and s' is the image distance

Front 2

Magnification

Back 2

Magnification is positive for upright images and negative for inverted images

Front 3

Sign Convention for Lenses

Back 3

f: Positive for converging lenses; Negative for diverging lenses
s: Positive in all cases
s': Positive if the image appears on the other side of the lens; negative if it appears on the same side of the lens
h: Always positive
h': Positive for upright images; negative for inverted images
One heuristic you can use to remember distance lengths is think about an "intuitive" case (which is positive) and a "nonintuitive" case (which is negative). When thinking about lenses, its intuitive to think about an image appearing on the other side (heuristic for s' sign).
Note: negative s' means virtual image!

Front 4

Sign Convention for Mirrors

Back 4

f: is positive for concave mirrors; negative for convex mirrors
s: always positive
s': positive if in front of the mirror; negative if behind the mirror (See heuristic)
h: Always positive
h': positive if image is upright; negative if the image is inverted
Heuristic for remembering s' sign convention: Think about "intuitive" (positive) vs. "nonintuitive" (negative) in terms of what you would expect from a mirror. You would expect a ray to be reflected in front of the mirror. Not behind it.

Front 5

Ray-Tracing Example For a converging lens

Back 5

Front 6

The eye

Back 6

the eye focuses by changing the focal length of the lens itself. It does this by changing the shape of the lens.

Front 7

Accommodation (in the eye)

Back 7

The process of changing the lens shape to focus on objects at different distances

Front 8

Far Point

Back 8

The most distant point a relaxed eye can see. This is infinity for normal vision. No limit because for an object at infinity, the light comes in parallel. Parallel lines always focus at the focal point of a lens

Front 9

Near Point

Back 9

The closest thing an eye can focus. Has a limit as to how much the eye can curve the lens. For normal vision, this is 25 cm.

Front 10

Eye focusing features

Back 10

The closer the object is to the eye, the more the muscle has to curve the lens. The closer the object is, the shorter the focal length of the eye

Front 11

Corrective lenses of myopia and hyperopia

Back 11

The myopic eye is too curved. To see distance object, diverging corrective lenses must be used. The hyperopic eye is not curved enough. To see near objects, converging lenses must be used

Front 12

Microscope

Back 12

L (Tube length) = s' (can be adjusted with a knob

See picture of microscope in book and notes. Couldn't put it here

Front 13

L (in a microscope)

Back 13

The length of the tube is the sum of image distance for the objective and the object distance for the eyepiece

Front 14

Through the (eyepiece) lens

Back 14

s is the image (s') formed by the objective lens. s' for the eyepiece is infinity! Rays come into your eye parallel. Ie. you can see the image with a relaxed eye. Also the image formed by the objective lens fall right on the focal point of the eyepiece. So s= f of the eyepiece. This will happen if you adjust the L.

Front 15

Refractive Power (Power)

Back 15

P=1/f
NOTICE: Power is reported in m^-1 (inverse meters). When doing your calculations. Make sure to convert your units to meters and THEN take the inverses.

Front 16

Power of two lenses

Back 16

The power of two lenses is the sum of their individual powers:
Ptotal = P1 + P2
Or
1/f(total) = 1/f(1) - 1/f(2)

Front 17

Finding the Powers of Corrective lenses

Back 17

using the principle of sum of powers:
1/f(expected) = 1/f(corrective) + 1/f(eye)

For farsighters: Power is postive
For nearsighters: power is negative

Front 18

Diffraction

Back 18

The "spreading out" of waves. Like what you would expect when ripples of water or light pass through a small hole. This only happens when the opening is small enough. On the order of how large the wavelengths are.

Front 19

Relating focal length and radius of curvature

Back 19

For spherical mirrors, the focal length is half of the radius of curvature r(i.e., f = r/2).

Front 20

index of refraction (n)

Back 20

the speed of a wave changes when it enters another material. The more dense the material, the greater the n

Front 21

changes in frequency with n

Back 21

frequency DOES NOT change as the wave moves from one medium to another

Front 22

changes in wavelength with n

Back 22

because frequency must stay constant, when light travels through material of differing reflective indices, and since light inherently changes speeds, according to the equation v=f(lambda), the wavelength must change inversely relative to the speed

Front 23

Interference fringes

Back 23

due to constructive and destructive interference

Front 24

Central Maximum

Back 24

The brightest fringe, at the midpoint of the viewing screen (m=0)

Front 25

Suppose the viewing screen moved closer to the double slits. What happens to the interference pattern?

Back 25

They get brighter and closer together

Front 26

Fringe spacing

Back 26

is independent of m. That is, any two bright fringes have the same spacing

Front 27

Phase change

Back 27

1 wavelength of phase change = the waves are "back in phase." They add and produce a bright fringe

1/2 wavelength change: "completely out of phase" completely destroy each other- no light, dark fringe

Front 28

Diffraction grading

Back 28

multiple-slit device. Light intensity pattern on the screen is due to the interference of N overlapped waves. Each slit is equally spaced (d)

Front 29

How do the slits produced by multiple slits (a diffraction grating) different from slits produced from a two-slit diffraction?

Back 29

1. The angles of constructive interference from diffraction grating are not small angles. You cannot use the small angle approximation
2. Bright fringes for a diffraction grating are narrower
3. Bright fringes for a diffraction grating are brighter:
I(max) = N^2I(1)

Front 30

Grating calculation

Back 30

calculating d: the length of the slit. Can be calculated from slits/mm

m: diffraction order. First order diffraction order: m=1. Unless otherwise stated, assume first order diffraction

Front 31

(lens' ) resolution

Back 31

it's ability to make out fine details of an object

Front 32

spherical aberration

Back 32

for lenses with spherical surfaces, there is no "one" focal point. The rays near the lens's center come to focus a bit further from the lens than those that pass near its edge. One way to overcome this is to not allow light in through the edges of the lens. The iris in the eye serves this purpose

Front 33

chromatic aberration

Back 33

different wavelengths focus at different points. Fix: achromatic doublet

Front 34

Dispersion

Back 34

The index of refraction of glass varies slightly with wavelength, The higher the lens's index of refraction, the more it bends incoming light rays. Because the index of refraction for violet light is larger than red light, a lens's focal length is slightly shorter for violet light than for red light

Front 35

Achromatic doublet

Back 35

two lenses used in combination to reduce chromatic aberrations. A converging lens is paired with a weak diverging lens so that the net effect is diverging. Also corrects spherical aberrations.

Front 36

Rayleigh's Criterion for Resolution

Back 36

(refer to figure on page 635):
1. Two objects are resolvable if their angular separation is alpha<theta, where theta 1 is 1.22lambda/D(diameter of the lens)
2. Two objects are not resolved if alpha< theta because their diffraction patterns are too overlapped.
3. The two objects are marginally resolvable if alpha=theta. The central maximum of one image falls exactly on top of the first dark fringe of the other image

Front 37

angular resolution of a telescope

Back 37

theta= 1.22lambda/D, where D is the lens diameter

Front 38

Resolving power

Back 38

minimum resolvable distance. The smaller the resolving power, the better the objective is at resolving small details. The minimal resolving power of a microscope is about half the wavelength of light. This is the fundamental limit set by the wave nature of light

Front 39

Huygen's Principle

Back 39

each point on a wave front is the source of a spherical wavelet. The wave front at a later time is tangent to all wavelets

Front 40

Diffraction patterns for single, double, and multiplel slit diffractions

Back 40

double slit and single slit uses the angle approxation. Angles must be in radians! For double slit, fringe spacing is equal

Front 41

Total internal reflection (critical angle)

Back 41

When the incidenced angle is greater then the critical angle. This can only happen if the index of reflraction in the second material is greater then the first (the one on top)

Front 42

Color and Dispersion

Back 42

deispersion depends on the index of refraction of the medium and the wavelength of the light. Long wavelenghts have lowest n (will disperse on top), high wavelengths have the highest n (will disperse on the bottom)

Front 43

Resolution for a telescope

Back 43

is equal to the angular distance for the first fringe on a circular apperture. The same equation is used

Front 44

Spherical Mirror Ray-Tracing

Back 44

Mirrors have four rays of interest:
1. Parallel Ray: coming in parallel, reflecting off through the focus
2. Focus Ray: Coming in through the focus and reflecting parallel
3. Center (of the Mirror) Ray: Hitting the mirror at the center of the optical axis (The incidence angle equals the reflected angle)
4. Center (of Curvature) Ray: comes in through the center of curvature and comes back in the same direction