Light Waves: An Introduction to Optics

Question 1

What was light thought to be initially?

Answer 1

Initially thought of as particles. BUt was growing evidence for a wave-like nature.

Question 2

What are the two wave equations for EM waves in a vacuum?

Answer 2

d^2 E/dx^2 = ϵ0μ0 d^2 E/dt^2.
Other is the same but with B instead of E, where ϵ0 and μ0 are the permittivity and permeability of free space respectively.

Question 3

What is the equation for wave speed in terms of ϵ0 and μ0?

Answer 3

c = 1/sqrt(ϵ0*μ0)

Question 4

How are electric and magnetic fields related?

Answer 4

They are perpendicular to eachother and they are perpendicular to the direction of propagation. If propagation is in x-direction, dEy/dx = -dBz/dt

Question 5

What is the equation relating the electic field E0 and magnetic field B0? What does this mean?

Answer 5

E0 = cB0. This means the magnetic field is small compared to E, so most of the effects we see arise from the E field interacting with electrons.

Question 6

What is the Poynting Vector?

Answer 6

The directional energy flux density (rate of change of energy transfer per unit area in direction of propagation)

Question 7

What is the equation for the Poynting vector?

Answer 7

S = 1/μ0 E X B

Question 8

What is the equation for intensity of the Poynting vector?

Answer 8

I = |Save| = 1/2 * ϵ0 * c * E0^2

Question 9

What is the momentum flow rate per unit area of EM waves?

Answer 9

1/A * dp/dt = S/c

Question 10

What is radiation pressure?

Answer 10

The pressure exerted upon any surface exposed to EM radiation.

Question 11

What equation do you get for an E field if you just consider the E field?

Answer 11

E = Eyj + Ezk

Question 12

What is the equation for Ey and Ez?

Answer 12

Ey = E0y cos(kx-ωt)
Ez = E0z cos(kx-ωt+φ)

Question 13

What is linearly polarised light?

Answer 13

When Ey and Ez are in phase. E-field always in same direction but magnitude changes over time.

Question 14

How would you look at the magnitude of the E-field over time in linearly polarised light?

Answer 14

Consider when Ey and Ez fluctuate between 1 and -1. (e.g. when Ey = 1 and Ez = -1, the light is diagonally upwards.

Question 15

What is circularly polarised light?

Answer 15

Ey and Ez have the same magnitude, but are pi/2 out of phase.

Question 16

What is left/right handed circularly polarised light?

Answer 16

Left-hand when φ = pi/2 (clockwise circle)

Right-hand when φ = -pi/2 (anti-clockwise circle)

Question 17

What is elliptical polarisation?

Answer 17

When Ey and Ez have different magnitudes and/or φ =/ npi/2

Question 18

What is a polarizer?

Answer 18

Filters which only allow through one type of polarization.

Question 19

What intensity of light does a linear polariser let through?

Answer 19

I = I0/2

only lets through one component of E-field

Question 20

What intensity of light does a linear polariser at an angle let through?

Answer 20

I = I0*cos^2(theta)

Question 21

What is a quarter wave plate?

Answer 21

Change the phase between Ey and Ez by pi/2. COnverts linear to circular and vice-versa.

Question 22

What should the distance between wave fronts be?

Answer 22

The wavelength.

Question 23

What is Huygen’s principle?

Answer 23

He proposed that every point on a wavefront acts as a point source, and the new wavefront is the sum of the wavelets - explains diffraction/refraction.

Question 24

Why does the apparent speed of light change due to interaction with matter?

Answer 24

The electric field interacts with the charges within a materialsuch that the light oscillates the charges within the material.

Question 25

What is the equation for the velocity of light in a medium?

Answer 25

v = 1/sqrt((ϵμ) = c/n = c/refractive index

Question 26

What is the equation for the power of a transmitted wave?

Answer 26

P = 4n1n2/(n1+n2)^2

Question 27

What is snells Law?

Answer 27

n1sin(theta1) = n2sin(theta2)

Question 28

What is the critical angle?

Answer 28

The angle at which n1/n2 * sin(theta) = 1, so sin(theta c) = n2/n1 - causes total internal reflection

Question 29

What is Brewster law?

Answer 29

tan(theta p) = nt/ni, where theta p is the polarisation angle.

Question 30

What is a birefringent material?

Answer 30

Material with two different refractive indexes (acts as a quarter wave plate).