Geometrical Optics 2

Question 1

What does it mean that rays are isochronous?

Answer 1

Each ray leaving the object point O reaches I in the same transit time by Fermat’s Principle.

Question 2

What would happen in an ideal imaging system?

Answer 2

Every ray from the object point would be intercepted by the system and pass through the conjugate image point.

Question 3

Nonideal images are formed due to…

Answer 3

Scattering, Diffraction and Aberrations

Question 4

Why are images said to be diffraction limited?

Answer 4

Every optical system only intercepts a fraction of the wavefront from the object leading to diffraction and a blurred image.

Question 5

(in words) what is the radius of curvature?

Answer 5

The radius of a circular arc that best describes the curve at a given point.

Question 6

What approximations lead to first-order optics at small angles?

Answer 6

sin 𝜙 = 𝜙 − 𝜙3/3! + 𝜙5/5! − ⋯ ≅ 𝜙
cos 𝜙 = 1 − 𝜙2/2! + 𝜙4/4! − ⋯ ≅ 1

Question 7

What is the relationship between the object and image distance and the radius of curvature for reflection at a convex spherical surface?

Answer 7

1/s - 1/s’ = -2/R

Question 8

Why do convex mirrors always produce virtual images?

Answer 8

Because the reflected rays always diverge

Question 9

Under what conditions would a concave mirror reflection produce a real image?

Answer 9

If the object is placed further away than the focal distance.

Question 10

What is the relationship between the object and image distance and the radius of curvature for reflection at a concave spherical surface?

Answer 10

1/s + 1/s’ = -2/R

Question 11

What happens where the radius of curvature goes to infinity?

Answer 11

We get a plane mirror and s=-s’

Question 12

(in words) what is the focal length of the mirror?

Answer 12

The image distance for an object at infinity

Question 13

What is the formula for focal distance?

Answer 13

f = -R/2

Question 14

For a concave mirror, is the focal length positive or negative?

Answer 14

positive

Question 15

For a convex mirror, is the focal length positive or negative?

Answer 15

negative

Question 16

What is the formula which relates the image and object distances to the focal length?

Answer 16

1/s + 1/s’ = 1/f

Question 17

(in words) what is the magnification

Answer 17

The ratio of the image to the object height

Question 18

Describe the sign convention for magnification

Answer 18

• negative value for inverted images
• positive value for upright images

Question 19

What is the formula for refraction at a spherical surface?

Answer 19

n1/s + n2/s’ = (n2 - n1)/R

Question 20

(in words) for a lens, what is the focal length

Answer 20

image distance for an object at infinity or object distance for an image at infinity

Question 21

What is the lensmaker’s equation

Answer 21

1/f = (n2-n1)/n1 (1/R1 - 1/R2)
this is often simplified to 1/f = 1/s + 1/s’

Question 22

How do you calculate the overall magnification from multiple lenses

Answer 22

m1 x m2 x …

Question 23

(in words) what is the lens power?

Answer 23

• a measure of the change of curvature of waves in object space to image space
• the reciprocal of the focal length

Question 24

How do you calculate the total power of lenses in physical contact?

Answer 24

1/ft = 1/f1 + 1/f2 + … = P1 + P2 + … = Pt