Light and Geometrical Optics

Question 1

In order for interference to occur, what conditions must hold:

Answer 1

• the interfering light sources must be coherent. This means they must constantly maintain the same phase relationship.
• The light coming from the two slits in Young’s double slit experiment are coherent because a single light source shines through both slits.
• the light source must be monochromatic (of single color/wavelength).

Question 2

Young’s Double Slit Interference

Answer 2

dsinθ = mλ

bright bands occur at m = 0, +/-1, +/-2 …etc.

dark bands occur at m = +/-0.5, +/-1.5, +/-2.5 …etc

Question 3

Thin Films

Answer 3

Thin films provide a means for interference to occur.

Light reflecting off the outer and inner boundary of a thin film interfere with each other.
A film of oil on water has the appearance of a swirly rainbow due to this interference.

Question 4

Diffraction Grating

Answer 4

Diffraction = light spreads out after passing through the slit, instead of going in a straight path.
Diffraction grating = a slab with many slits close together.
The equation for a diffraction grating is the same as the double-slit experiment:
dsinθ = mλ

Question 5

Single Slit

Answer 5

Light shining through a single slit casts a central bright band followed by a series of maximas and minimas on either side.

The equation for a single slit diffraction is different from the equation for the double slit.

asinθ = mλ

a is the width of the slit.

Maxima occurs for m = 0 (big central maxima), +/-1.5, +/-2.5 , etc.

Minima occurs for m = +/-1, +/-2, +/-3, etc.

Question 6

Polarization of Light: polarized vs unpolarized light

Answer 6

Unpolarized light = light with electric field oscilating in many planes.

Polarized light = light with electric field oscilating in only one plane.

Question 7

Selective absorption

Answer 7

pass light through polarizer that absorbs all but light with electric field in one plane

Question 8

Reflection

Answer 8

at a certain polarizing angle, all reflected light is polarized.

Question 9

Double refraction

Answer 9

birefringent materials have two indices of refraction that splits the incident light into two rays polarized perpendicular to each other

Question 10

Scattering

Answer 10

air molecules scatter light, which becomes polarized.

Question 11

Doppler effect

Answer 11

Red shift = frequency decreases = occurs when source and observer is moving away from each other.

Blue shift = frequency increases = occurs when source and observer is moving toward each other.

Question 12

Energy per photon

Answer 12

E = hv where h is Planck’s Constant (6.6 x 10-34 m² kg/s)

Question 13

Reflection from plane surface

Answer 13

angle of incidence equals angle of reflection

Question 14

Refraction

Answer 14

Snell’s Law: n₁sinθ₁ = n₂sinθ₂

Question 15

Dispersion

Answer 15

change of index of refraction with wavelength; blue light refracts more than red light in a prism.

Question 16

Conditions for total internal reflection

Answer 16

1. Going from a medium of high index of refraction to a medium of low index of refraction.
2. Angle of incidence > critical angle.
3. Find the critical angle by: n1sinθc = n2sin90° n1 > n2 θc = critical angle

Question 17

Concave Mirror

Question 18

Convex Mirror

Question 19

Convex Lens - Real Image

Question 20

Convex Lens - Virtual Image

Question 21

Conave Lens - Virtual Image

Question 22

Thin Lens Equation

Question 23

Converging and Diverging Lenses