1 - Geometrical and Physical Optics

Question 1

What is the law of reflection?

Answer 1

The law of reflection states that the angle of reflection is equal to the angle of incidence:
θi = θr. The angle θi refers to the angle of the incoming ray of light makes with the surface
normal and θr the angle the departing ray makes with the surface normal.

Question 2

What is the law of refraction?

Answer 2

The law of refraction, which is generally known as Snell’s law, governs the behaviour of light-rays as they propagate across a sharp interface between two transparent dielectric media.

Question 3

Why does refraction occur?

Answer 3

Refraction occurs because the speed of light is different in different media.

This causes light to bend toward the surface normal when travelling from a less to a more dense medium (i.e. across a boundary where the refractive index increases) or away from the surface normal when travelling from a more to less dense medium (i.e. across a boundary where the refractive index decreases).

The refractive index of a medium is defined as n=c/v where c is the speed of light in a vacuum and v is the speed of light in the medium.`

Question 4

What is dispersion?

Answer 4

When light consisting of a range of wavelengths (for example, white light) passes through a medium, every wavelength is refracted at a slightly different angle since the refractive index depends on the incoming wavelength. This is dispersion.

Question 5

What is Snell’s law?

Answer 5

Snell’s law describes the law of refraction. It quantitatively expresses how the angle of incidence relates to the angle of refraction when light passes from one medium to another across an abrupt boundary: ni sin θi = nr sin θr.

n_i: refractive index of medium where ray originates
n_r: refractive index of the medium the ray enters
θ_i: angle of incidence (of the ray with respect to the surface normal)
θ_i: angle of refraction (of the ray with respect to the surface normal)

Question 6

What is Total Internal Reflection?

Answer 6

Total internal reflection occurs when a ray travels across a boundary from high to low refractive index and the angle of incidence surpasses the critical angle. The critical angle is the angle of incidence which produces an angle of refraction equal to π/2.

Question 7

What are the two types of thin lenses?

Answer 7

Convergent and Divergent Lenses

Question 8

How do convergent lenses work?

Answer 8

A converging lens is a lens that converges rays of light that are travelling parallel to its principal axis. Converging lenses can be identified by their shape; they are relatively thick across their middle and thin at their upper and lower edges.

Question 9

How do divergent lenses work?

Answer 9

A diverging lens is a lens that diverges rays of light that are travelling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are relatively thin across their middle and thick at their upper and lower edges.

Question 10

What is the lens formula?

Answer 10

1/d_o+1/d_i=1/f

d_o = Object distance
d_i = Image distance
f = focal length

Question 11

What is the magnification equation?

Answer 11

M=h_i/h_o=-d_i/d_o

h_o = Object height
h_i = Image height
d_o = Object distance
d_i = Image distance

Question 12

How do you tell if a lens is converging or diverging?

Answer 12

Given the focal length,

If f>0 –> converging

If f<0 –> diverging

Question 13

How do you express the electric field of a light wave?

Answer 13

E = A/r * cos( omega ( t - r/c ) )

Question 14

What is the expression for angular frequency?

Answer 14

omega = 2 * pi * f

Question 15

What is the expression for the wave number k?

Answer 15

k = (2 * pi) / lambda

Question 16

What is an expression for the speed of light c, containing angular frequency and wave number?

Answer 16

c = omega / k

Question 17

What is the relationship between the maximum Electric field and intensity (irradiance)?

Answer 17

I = 1/2 * epsilon_0 * c * E^2 _max

Question 18

What are the units of irradiance?

Answer 18

W * m^-2

Question 19

What is epsilon naught?

Answer 19

The permittivity of free space:

8.854187817 C^2 / N * m^2

Question 20

What is the principle of superposition?

Answer 20

The superposition principle states that when two or more waves overlap in space, the resultant disturbance is equal to the algebraic sum of the individual disturbances.

Question 21

What is Huygen’s Principle?

Answer 21

Huygens’ principle, in optics, a statement that all points of a wavefront of light in a vacuum or transparent medium may be regarded as new sources of wavelets that expand in every direction at a rate depending on their velocities.

Question 22

What is diffraction?

Answer 22

Diffraction refers to the effects of a wave interacting with an obstacle or slit. In the case of light, it refers to the bending of light that occurs when it interacts with a sharp boundary, leading to the well-known diffraction pattern on a screen when passing through one or multiple slits.

Question 23

What is interference?

Answer 23

Interference is the phenomenon in which two waves superpose to form the resultant wave of the lower, higher or same amplitude. The most commonly seen interference is an optical interference or light interference.

This is because light waves are randomly generated every which way by most sources. This means that light waves coming out of a source do not have a constant amplitude, frequency or phase.

Question 24

What do the Fraunhofer and Fresnal conditions refer to?

Answer 24

The Fraunhofer and Fresnel conditions refer to the distance that a screen must be placed in a diffraction set-up in order to achieve a specific type of diffraction pattern.

The far-field pattern is known as the Fraunhofer diffraction pattern and the near field pattern is known as the Fresnel diffraction pattern; the transition from a Fresnel to Fraunhofer pattern is usually taken to be at distances larger than the Fresnel parameter:

S = D^2 / 4 * λ

Where D is the width of the slit and λ is the wavelength of light.

Question 25

What is the period formula?

Answer 25

T = lambda / velocity

Question 26

What formula describes when constructive interference occurs?

Answer 26

r_2 - r_1 = m * lambda

For m = 0, +-1, +-2, …

Question 27

What formula describes when destructive interference occurs?

Answer 27

r_2 - r_1 = (m + 1/2) * lambda

For m = 0, +-1, +-2, …