Basic Geometrical Optics

Question 1

State the law of reflection and how it applies to light rays at plane and spherical surfaces.

Answer 1

Law of reflection: When a ray is reflected on a smooth surface is the angle of reflection equal to the angle of incidence, the incident ray, reflected ray and the normal to the surface all lie in the same plane.

Curved surface: at the point of the surface draw a surface tangent, draw the normal to the tangent on the point of the surface (it should go through the centre of the surface), now apply law of reflection.

Question 2

State and show with appropriate drawings how it applies to light rays at plane and spherical surfaces.

Answer 2

Sin (angle of incidence) / sin (angle of refraction)
= n of incident medium / n of refracting medium.
usually written as n_i sin i = n_r sin r

Question 3

Define index of refraction.

Answer 3

It distinguishes the media in the interface. For any transparent optical medium it’s defined as the ratio of the speed of light in vacuum to its speed in the medium.
n = c /v Greater value -> more bend.
light goes from lower to higher bends towards the normal.
Light higher n -> lower n bends away from the normal.

Question 4

Calculate the critical angle of incidence for the interface between two optical media and describe the process of total internal reflection.

Answer 4

Light that travels from medium with higher index to lower index can bend by 90 degrees - the angle causing this is the critical angle.

Total internal reflection: Rays with a incidence higher than the critical angle will be totally reflected into the media it originated from. 
n_i sin(i) = n_r sin(90) -> i_c = sin^-1 (n_r / n_i)

Question 5

Calculate the minimum angle of deviation for a prism and show how this angle can be used to determine the refractive index of a prism material.

Answer 5

Minimum angle of deviation δ: The min angle a wave can enter a prism and be refracted instead of reflected.
Apex = pointed tip of cone. independent of wavelengt
refactive index = sin((prism apex angle + minimum angle of deviation)/2 ) / sin (prism apex angle / 2)

Question 6

Describe what is meant by Gaussian or paraxial optics

Answer 6

a

Question 7

Describe the relationship between collimated light and the focal points of convex and concave mirrors.

Answer 7

s

Question 8

Use the mirror equations to determine location, size, orientation, and nature of images formed with spherical mirrors.

Answer 8

d

Question 9

Distinguish between a thin lens and a thick lens.

Answer 9

f

Question 10

Describe the shapes of three typical converging (positive) thin lenses and three typical diverging (negative) thin lenses

Answer 10

g

Question 11

Describe the f-number and numerical aperture for a lens and explain how they control image brightness

Answer 11

h

Question 12

Describe the relationship between collimated light and the focal points of a thin lens.

Answer 12

j

Question 13

Use the lensmaker’s equation to determine the focal length of a thin lens.

Answer 13

k

Question 14

Use the thin-lens equations to determine location, size, orientation, and nature of the images formed by simple lenses.

Answer 14

l

Question 15

Describe dispersion.

Answer 15

The variation of refractive index n with wavelength λ is called dispersion.

Question 16

Draw a concave and a convex mirror, mark the mirror vertex V, the center of curvature C, and the focal point F on each drawing.

Answer 16

ö