Q: A glass rod has a surface power $$F = -4.00\ \mathrm{D}$$ and the secondary focal length $$f' is $$measured as $$-0.25\ \mathrm{m}. $$What is the index of refraction $$n' of $$the rod if the first medium is air ($$n=1$$)?

$$n' = 1.0 + 4.00 \times 0.25 = 2.0$$

Question 1

Which of the following statements correctly describes the sign convention for distances in refraction at a single spherical refracting surface?

Accepted Answer

Distances measured in the direction of light travel are positive.

Question 2

A convex spherical glass surface separates air ($$n=1) $$from glass ($$n'=1.5). If $$the radius of curvature is $$0.02\ \mathrm{m}$$, what is the surface power $$F of $$the surface?

Accepted Answer

$$F = \dfrac{1.5 - 1}{0.02} = 25\ \mathrm{D}$$

Question 3

Which of the following best describes the behavior of plane waves incident from air onto a convex spherical glass surface?

Accepted Answer

The waves converge after passing through the surface.

Question 4

Given an object in air placed $$0.5\ \mathrm{m} in $$front of a plastic rod ($$n' = 1.49) $$with a surface power $$F = -3.00\ \mathrm{D}$$, what is the image position $$l'$$?

Accepted Answer

$$l' = -0.298\ \mathrm{m}$$

Question 5

What is the formula for the surface power $$F of a $$single spherical refracting surface?

Accepted Answer

$$F = \dfrac{n' - n}{r}$$

Question 6

A concave spherical surface separates air ($$n=1) $$from polycarbonate ($$n'=1.586) $$with a radius of curvature $$r = 0.04\ \mathrm{m}. An $$object is $$0.08\ \mathrm{m} in $$front of the surface. What is the image position $$l'$$?

Accepted Answer

$$l' = +0.738\ \mathrm{m}$$

Question 7

Which equation correctly represents the Gaussian Imaging Equation for a single spherical refracting surface?

Accepted Answer

$$L + F = L'$$

Question 8

If the object is at infinity ($$l = \infty$$), what is the emergent vergence $$L'$$ for a convex surface?

Accepted Answer

$$L' = F$$

Question 9

For a concave surface, if the image is at infinity ($$l' = \infty$$), what is the incident vergence $$L$$?

Accepted Answer

$$L = -F$$

Question 10

Which of the following best describes the lateral magnification ($$LM) $$for a single spherical refracting surface?

Accepted Answer

$$LM = \dfrac{h'}{h} = \dfrac{nl'}{n'l}$$

Question 11

A student claims that for a convex surface, parallel rays entering from air into glass will diverge after refraction. Is this correct?

Accepted Answer

No, the rays will converge after refraction.

Question 12

If the radius of curvature of a surface is doubled while keeping the indices of refraction constant, what happens to the surface power $$F$$?

Accepted Answer

The surface power is halved.

Question 13

Which of the following is true about the sign of the radius of curvature $$r$$ for a convex surface (as seen by light traveling from left to right)?

Accepted Answer

$$r is $$positive.

Question 14

A glass rod has a surface power $$F = -4.00\ \mathrm{D}$$ and the secondary focal length $$f' is $$measured as $$-0.25\ \mathrm{m}. $$What is the index of refraction $$n' of $$the rod if the first medium is air ($$n=1$$)?

Accepted Answer

$$n' = 1.0 + 4.00 	imes 0.25 = 2.0$$

Question 15

Which of the following best describes the image formed by a concave spherical surface when plane waves enter from air?

Accepted Answer

The image is virtual and located in object space.

Question 16

A student measures the object distance $$l as$$ $$-0.1\ \mathrm{m}$$ for a convex surface. What does the negative sign indicate?

Accepted Answer

The object is located opposite to the direction of light travel.

Question 17

If the emergent vergence $$L' is $$positive, what does this indicate about the nature of the image?

Accepted Answer

The image is real and located in the second medium.

Question 18

Which of the following is the correct formula for incident vergence $$L$$?

Accepted Answer

$$L = \dfrac{n}{l}$$

Question 19

A convex glass surface ($$n' = 1.5) $$has a secondary focal length $$f' = 0.1\ \mathrm{m}. $$What is the surface power $$F$$?

Accepted Answer

$$F = \dfrac{1.5}{0.1} = 15\ \mathrm{D}$$

Refraction at a Single Spherical Surface: Principles, Formulas, and Applications

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