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

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- 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).

Young's Double Slit Interference

dsinθ = mλ

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

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

Thin Films

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.

Diffraction Grating

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**

Single Slit

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.

Polarization of Light: polarized vs unpolarized light

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

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

Selective absorption

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

Reflection

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

Double refraction

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

Scattering

air molecules scatter light, which becomes polarized.

Doppler effect

__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.

Energy per photon

E = hv where h is Planck's Constant (6.6 x 10-34 m^{2} kg/s)

Reflection from plane surface

angle of incidence equals angle of reflection

Refraction

Snell's Law: n_{1}sinθ_{1} = n_{2}sinθ_{2}

Dispersion

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

Conditions for total internal reflection

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

Concave Mirror

Convex Mirror

Convex Lens - Real Image

Convex Lens - Virtual Image

Conave Lens - Virtual Image

Thin Lens Equation

Converging and Diverging Lenses