Quiz: Apparent Depth and Total Internal Reflection — 13 questions

1. Light travels from a medium with refractive index n₁ to a rarer medium with refractive index n₂; which expression gives the critical angle C?

A. sin C = n₁n₂

B. sin C = n₂/n₁

C. sin C = n₁/n₂

D. sin C = 1/(n₁+n₂)

Answer: (B)

Explanation

For light passing from a denser medium of refractive index n₁ to a rarer medium of refractive index n₂, the critical angle satisfies sin C = n₂/n₁.

2. What is the critical angle for light traveling from a denser medium into a rarer medium?

A. The incidence angle at which the refracted ray bends toward the normal

B. The incidence angle at which the refracted ray travels along the interface

C. The refracted angle at which the ray returns into the denser medium

D. The incidence angle at which the reflected ray disappears completely

Answer: (B)

Explanation

The critical angle is the angle of incidence in the denser medium for which the refracted ray travels along the interface at 90°. Total internal reflection begins only when the incidence angle increases beyond this value.

3. For an object beneath a plane water–air interface viewed perpendicularly from air, how is refractive-index ratio related to real and apparent depth?

A. It equals the sum of real and apparent depth

B. It equals the difference between real and apparent depth

C. It equals real depth divided by apparent depth

D. It equals apparent depth divided by real depth

Answer: (C)

Explanation

For perpendicular observation at a plane interface, the refractive-index ratio equals real depth divided by apparent depth. Neither depth is measured from the observer’s eye.

4. What does apparent displacement describe in refraction at an interface?

A. The distance from the observer’s eye to the virtual image

B. The change in refractive index across the interface

C. The distance between the interface and the real object only

D. The positional shift between a real object and its virtual image

Answer: (D)

Explanation

Apparent displacement is the shift between the real object and the virtual image produced by refraction. Apparent depth instead refers to the image’s distance from the interface.

5. Water fills a 24 cm-deep container, and the container is to appear half-filled when viewed from air. What real water depth is required, approximately, if the refractive index of water is 4/3?

A. 18.00 cm

B. 10.28 cm

C. 13.72 cm

D. 12.00 cm

Answer: (C)

Explanation

The apparent water depth must be 24 − x, so 4/3 = x/(24 − x), yielding x ≈ 13.72 cm. A true 12 cm half-fill would not appear half-filled.

6. What happens to the apparent depth of an object in a denser medium when it is viewed from a rarer medium?

A. It remains equal to the real depth, so no virtual image forms

B. It becomes smaller, so the virtual image appears closer to the interface

C. It becomes zero, so the object appears exactly at the interface

D. It becomes larger, so the virtual image appears farther from the interface

Answer: (B)

Explanation

When viewed from a rarer medium, an object in a denser medium appears at a smaller depth. Its virtual image therefore lies closer to the interface.

7. Under which condition does total internal reflection occur?

A. Light travels from a denser medium to a rarer medium with an incidence angle greater than the critical angle

B. Light travels between two media with identical refractive indices at a large incidence angle

C. Light travels from a rarer medium to a denser medium at any incidence angle

D. Light travels from a denser medium to a rarer medium at an incidence angle equal to the critical angle

Answer: (A)

Explanation

Total internal reflection occurs when light travels from a denser to a rarer medium and the incidence angle exceeds the critical angle. At the critical angle itself, a grazing refracted ray still exists.

8. Under which conditions can the simplified real-depth/apparent-depth relation be applied directly?

A. At a plane surface with perpendicular viewing from the denser medium

B. At any interface regardless of viewing direction

C. At any curved surface with oblique viewing from air

D. At a plane surface with perpendicular viewing from air

Answer: (D)

Explanation

The simplified relation requires a plane interface, perpendicular observation, and an observing eye in air. It cannot be applied generally to curved surfaces or arbitrary viewing angles.

9. When a denser medium is viewed from air, which expression gives its refractive index?

A. The difference between real and apparent depth

B. Real depth multiplied by apparent depth

C. Real depth divided by apparent depth

D. Apparent depth divided by real depth

Answer: (C)

Explanation

With air as the rarer medium, the refractive index is n = real depth/apparent depth. Reversing the ratio gives the reciprocal rather than the refractive index.

10. For light traveling from a material of refractive index n into air, which equation should be used to calculate the critical angle?

A. sin C = n²

B. sin C = 1/n

C. sin C = n

D. sin C = 1 − n

Answer: (B)

Explanation

When the rarer medium is air, its refractive index is taken as approximately 1, so the general relation becomes sin C = 1/n. The ratio n₂/n₁ is needed when the rarer medium is not air.

11. A layer of thickness t and refractive index n is viewed from air. Which formula gives its apparent displacement?

A. d = t(1 − 1/n)

B. d = t/n

C. d = t(1 + 1/n)

D. d = t(n − 1)

Answer: (A)

Explanation

For a layer viewed from air, the apparent displacement is d = t(1 − 1/n). The expression accounts for the reduction in apparent depth caused by refraction.

12. What happens as the incidence angle increases from below the critical angle?

A. The refracted ray immediately disappears as soon as the incidence angle increases

B. The refracted angle decreases until the ray returns toward the normal

C. The refracted angle increases until it reaches 90°, after which total internal reflection occurs

D. The refracted angle remains fixed until the ray is reflected

Answer: (C)

Explanation

As the incidence angle increases, the refracted angle also increases until the ray reaches the interface at 90°. Any further increase in incidence angle produces total internal reflection.

13. Which comparison of glass–air and water–air critical angles is correct for yellow light?

A. Glass–air is approximately 42°, while water–air is approximately 48°35′

B. Glass–air and water–air both have a critical angle of approximately 62°44′

C. Glass–air is approximately 48°35′, while water–air is approximately 42°

D. Both pairs have a critical angle of approximately 45°

Answer: (A)

Explanation

For yellow light, the glass–air critical angle is approximately 42°, using sin C = 2/3, while the water–air critical angle is approximately 48°35′, using sin C = 3/4.