Lecture 1 · Practice

Fundamental Optics Principles: Practice Worksheet

Show your work. Write vergences and powers with a sign (+ or −) and units (D).
Convert distances to meters before taking a reciprocal.
Light travels left to right. Distances to the left of a lens are negative.
Use n(air) = 1.000 and n(water) = 1.333 unless told otherwise. c = 3.00 × 10⁸ m/s.
Check your answers in the interactive worksheet on the course site.
Parts F and G are extensions. They introduce the Lensmaker’s and Thin Lens equations using the vergence ideas from this lecture.

Part A

Vergence & Collimation

V = \frac{1}{d\,(\text{m})}

Diverging light: negative · Converging light: positive · Collimated: 0 D

A point source is 2 m from an observer. What vergence reaches the observer?

2 pts

What is the vergence of light 25 cm from a point source?

2 pts

A lens focuses light to a point 50 cm away. What vergence does the light have as it leaves the lens?

2 pts

An observer measures −0.10 D of divergence from a point source. How far away is the source, in meters?

2 pts

Which observer receives light with the greatest magnitude of vergence?

1 pt

Optical infinity is 6 m. What is the actual vergence of light from a point source 6 m away?

2 pts

Collimated light has a vergence of:

1 pt

Part B

Reflection

\theta_i = \theta_r

Angles from the normal · angle from surface = 90° − angle from normal

A ray strikes a mirror 25° from the surface. At what angle does it leave, measured from the surface?

2 pts

A ray strikes a mirror 35° from the normal. What angle does the reflected ray make with the mirror’s surface?

2 pts

A ray strikes a mirror 30° from the normal. What is the angle between the incident ray and the reflected ray?

2 pts

Challenge: a ray strikes a mirror 20° from the surface. What is the angle between the incident and reflected rays?

3 pts

Part C

Refraction, Snell’s Law & Index of Refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

n = \frac{c}{v}

Light passes from air into water at 30° from the normal. What is the angle of refraction?

3 pts

Light passes from air into crown glass (n = 1.523) at 45°. What is the angle of refraction?

3 pts

How fast does light travel in water (n = 1.333)? Give your answer in units of 10⁸ m/s.

2 pts

× 10⁸ m/s

Light travels at 1.89 × 10⁸ m/s in a lens material. What is its index of refraction, and which material is it?

2 pts

When light passes from air into water, it bends:

1 pt

Light leaves water and enters air, striking the surface at 30° from the normal. What is the angle of refraction in air?

3 pts

A ray in air hits an unknown material at 40° and refracts to 25°. What is the material’s index?

3 pts

Challenge: beyond what angle in water (from the normal) does light fail to escape into air at all?

3 pts

Part D

Lenses, Focal Points & the Vergence Equation

P = \frac{1}{f\,(\text{m})}

V = U + P

U = vergence entering the lens · V = vergence leaving

A lens converges collimated light to a point 20 cm behind it. What is its power?

2 pts

After passing through a lens, collimated light appears to diverge from a point 50 cm in front of it. What is the lens power?

2 pts

What is the focal length of a +8.00 D lens, in centimeters?

2 pts

A point source sits 25 cm to the left of a +4.00 D lens. What vergence leaves the lens?

3 pts

The same source is moved to 50 cm left of the +4.00 D lens. What vergence leaves the lens?

3 pts

For question D5, how far to the right of the lens does the light come to a focus, in centimeters?

2 pts

Converging light of +2.00 D strikes a −5.00 D lens. What vergence leaves the lens, and is it converging or diverging?

3 pts

Using this lecture’s convention, the focal point where collimated light seems to originate for a negative lens is:

1 pt

Part E

Applications & Concepts

Why can a high-index lens be thinner than a CR-39 lens of the same prescription?

1 pt

A spear-fisher sees a fish ahead and below. To hit it they should aim:

1 pt

In a primary rainbow, which color appears on the outside (top) of the bow?

1 pt

Which lens material is the usual choice for a child’s safety glasses?

1 pt

True or false: a lens with a focal length of 2 m is stronger than a lens with a focal length of 0.5 m.

1 pt

In two or three sentences, explain why a mirage appears on a hot road.

3 pts

Part F

Extension: The Lensmaker’s Equation

A lens's power depends on its material (n) and the curvature of its two surfaces. For a thin lens in air:

P = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)

R₁ is the front surface radius and R₂ the back surface radius, in meters. A radius is positive when its center of curvature lies to the right of the surface, and negative when it lies to the left. A flat surface has R = ∞ (so 1/R = 0).

A biconvex lens has n = 1.50, R₁ = +20 cm and R₂ = −20 cm. What is its power?

3 pts

The same shape is made in 1.74 high-index plastic. What is its power now?

3 pts

A plano-concave polycarbonate lens (n = 1.586) has a flat front (R₁ = ∞) and a back surface with R₂ = +10 cm. What is its power?

3 pts

Design problem: what front radius (in cm) gives a plano-convex crown glass lens (n = 1.523, flat back) a power of +4.00 D?

3 pts

Part G

Extension: The Thin Lens Equation

The thin lens equation is the vergence equation written with distances. The object distance u is negative for a real object to the left of the lens; a positive image distance v means a real image to the right.

\frac{1}{v} = \frac{1}{u} + \frac{1}{f} \quad\Longleftrightarrow\quad V = U + P \qquad m = \frac{v}{u}

Magnification m: negative means inverted, positive means upright; |m| > 1 means enlarged.

An object is 40 cm to the left of a +5.00 D lens. Where is the image? (Signed distance in cm.)

3 pts

What is the magnification of the image in G1?

2 pts

The object moves to 10 cm left of the same +5.00 D lens. Where is the image now? (Signed distance in cm.)

3 pts

An object is 50 cm to the left of a −4.00 D lens. Where is the image? (Signed distance in cm.)

3 pts

Challenge: where must an object be placed so a +10.00 D lens forms a real image 30 cm to its right? (Signed distance in cm.)

3 pts

Your score

0 of 93 points · 0 of 42 questions checked

Fundamental Optics Principles: Practice Worksheet

Show your work. Write vergences and powers with a sign (+ or −) and units (D).

Convert distances to meters before taking a reciprocal.

Light travels left to right. Distances to the left of a lens are negative.

Use n(air) = 1.000 and n(water) = 1.333 unless told otherwise. c = 3.00 × 10⁸ m/s.

Check your answers in the interactive worksheet on the course site.

Parts F and G are extensions. They introduce the Lensmaker’s and Thin Lens equations using the vergence ideas from this lecture.