OP - Principles of Paraxial Optics - Week 3

Question 1

Define a paraxial ray.

Answer 1

A ray that travels very close to the optical axis, and always stay close to the axis.

Question 2

Why are paraxial rays significant?

Answer 2

All the angles are very small relative to the optical axis, and so the trigonometric function more or less equals the angle. ie. sin(x) = x. This only occurs at small angles.
This only applies to radians, and not degrees.

Question 3

Describe taylor series approximations for sin(x).

Answer 3

sin(x) = x - x^3/3! + x^5/5! + x^7/7! + …

Allows greater and greater approximations for sin (x).

Question 4

Describe how snells law changes with respect to paraxial rays.

Answer 4

n’i’ = ni

Question 5

Define the paraxial refraction equation.

Answer 5

n’u’ - nu = -hF

Question 6

Define F and its equation.

Answer 6

F is the power of a surface.

F = C (n’ - n)

Question 7

Define C’s equation.

Answer 7

C = curvature
C = 1 / r

Question 8

Describe the opening and closing equations (hint h=)

Answer 8

Opening
h = -ul
Closing
h = -u’l’

Question 9

Describe the equation that proves paraxial rays are coincident.

Answer 9

(n’/l’) - (n/l) = F

Question 10

Describe the paraxial transfer equation.

Answer 10

h’ = h + u’d

Question 11

Describe the steps of ray-tracing through a number of steps.

Answer 11

• Choose a ray using the opening equation.
• Apply paraxial refraction equation to find u’
• Apply the paraxial transfer equation to find h’
• Repeat from step one, transforming u’ to u, h’ to h
• If final refraction, apply closing equation