Snell's Law

n

c

λ

I

Where n is the refraction index of the material

_{1}Sin [θ_{1 }] = n_{2}Sin [θ_{2 }]c

_{n }= c / nλ

_{n }= λ / nI

_{θ }= I_{0 }E^{2 }_{θ }/ E^{2 }_{0 }Where n is the refraction index of the material

Lens Equation:

1 / d

m = - d

Where d

_{i }+ 1 / d_{o }= 1 / fm = - d

_{i }/ d_{o }Where d

_{i }is the distance to the image and d_{o }is the distance to the object. m represents the magnification of the object in comparison to the objects actual size.
Lens maker Equation:

1 / f = (n - 1) (1 / R

r = f / 2

f is the focal length, and r is the radius of curvature. The focal length is the distance at which the parallel rays of light travelling through the lens will converge to a point. The radius of curvature represents the radius of the sphere that the lens could make if it was continued to a sphere.

_{1 }+ 1 / R_{2 })r = f / 2

f is the focal length, and r is the radius of curvature. The focal length is the distance at which the parallel rays of light travelling through the lens will converge to a point. The radius of curvature represents the radius of the sphere that the lens could make if it was continued to a sphere.

Interference and Diffraction-

Double Slit interference:

I

d Sin[θ] = m λ / Maxima

d Sin[θ] = (m +1/2) λ / Minima

_{θ }= I_{0 }[Cos(δ / 2)]^{2 }d Sin[θ] = m λ / Maxima

d Sin[θ] = (m +1/2) λ / Minima

Single Slit diffraction:

I

D Sin[θ] = (m +1/2) λ / Maxima

Note - θ = 0 is the central and highest peak

D Sin[θ] = m λ / Minima

_{θ }= I_{0 }[Sin(Β/2) / (Β / 2)]^{2 }D Sin[θ] = (m +1/2) λ / Maxima

Note - θ = 0 is the central and highest peak

D Sin[θ] = m λ / Minima

Single and double slit effects:

I

_{θ }= I_{0 }[Sin(Β/2) / (Β / 2)]^{2 }[Cos(δ / 2)]^{2}
Diffraction grating:

Sin (θ) = m λ / d

R = λ / (Δ λ) = N m

R is the resolving power of the lens

R is the resolving power of the lens

Circular hole diffraction

θ = 1.22 λ / D

Polaroids

I = I

_{0 }(Cos[θ])^{2}
Relativity

Minkowski space-This is the setting in which relativistic calculations are done. Points in Minkowski space are represented by a 4-vector which defines position in x, y, z and time, and is represented by the Minkowski metric, which is defined as:

[-1 0 0 0]

| 0 1 0 0|

| 0 0 1 0|

[ 0 0 0 1]

| 0 1 0 0|

| 0 0 1 0|

[ 0 0 0 1]

Invariance of the interval:

(Δs)

(Δs')

The invariance of the interval is also known as the line element of the minkowski metric.

^{2 }= (Δx)^{2 }- (c Δt)^{2 }(Δs')

^{2 }= (Δs)^{2 }The invariance of the interval is also known as the line element of the minkowski metric.

Lorentz Transformations-

ct = γ ( v x' / c + c t ' )

x = γ ( x' + v t ' )

y = y'

z = z'

x = γ ( x' + v t ' )

y = y'

z = z'

This is assuming your working in a frame where there is movement in only one direction, however due to the isotropy of space, you can almost always make this assumption.

γ = 1 / [1 - (v / c)

This is known as the lorentz factor, which is used in the lorentz transformation.

^{2 }]^{1/2 }This is known as the lorentz factor, which is used in the lorentz transformation.

Velocity addition formulas-

u

u

u

_{parallel }= (u_{parallel }' + v) / (1 + (u_{x }' v / c^{2 }))u

_{perpendicular }= (u_{perpendicular }') / [γ (1 + (u_{perpendicular }' v / c^{2 }))]
Contraction

L' = L / γ

Where L' is the length of the moving object as observed by the stationary frame.

Δt' = γ Δt

Where t ' is the length of time experienced by an observer in the stationary frame.

Where L' is the length of the moving object as observed by the stationary frame.

Δt' = γ Δt

Where t ' is the length of time experienced by an observer in the stationary frame.

Stationary frames are described by no acceleration.

Non constant velocity

τ = ∫ [1 - ( v

^{2 }(t) / c^{2 })]^{1/2 }dt
Momentum and Energy

p = γ m v

E = γ m c

E

KE = E - m

E = γ m c

^{2 }= [m^{2 }c^{4 }+ |p|^{2 }c^{2 }]E

^{2 }= m^{2 }c^{4 }+ p^{2 }c^{2 }KE = E - m

^{2 }c^{2 }= (γ - 1) m c^{2}
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