A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material?单项选择题
A
1.40
B
1.43
C
1.44
D
1.48

Question

A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material?单项选择题

A

1.40

B

1.43

C

1.44

D

1.48

BlackTom AI · Accepted Answer

Law of reflection gives θr = 56.0° (the reflected ray makes the same angle to the normal as the incident ray). Because the reflected and refracted beams are observed to be perpendicular, the angles they make with the normal satisfy θr + θt = 90.0°, so the refracted angle θt = 90.0° − 56.0° = 34.0°.

Relevant concepts:
- Law of reflection: θincident = θreflected.
- Snell’s law (refraction): n1 sin θ1 = n2 sin θ2, where n1 and n2 are indices of refraction and θ1, θ2 are angles measured from the normal.
- For air, take n1 ≈ 1.00.

Step-by-step reasoning and calculation:
1. θr = θ1 = 56.0° (reflection law).
2. Perpendicular rays ⇒ θr + θt = 90.0° ⇒ θt = 90.0° − 56.0° = 34.0°.
3. Apply Snell’s law with n1 = 1.00, θ1 = 56.0°, θ2 = 34.0°:
   n2 = n1 (sin θ1 / sin θ2) = 1.00 × (sin 56.0° / sin 34.0°).
4. Evaluate sines (to sufficient precision):
   sin 56.0° ≈ 0.8290376
   sin 34.0° ≈ 0.5591929
   n2 ≈ 0.8290376 / 0.5591929 ≈ 1.4820.
5. Rounding to two decimal places gives n2 ≈ 1.48.

Why this answer is correct:
The geometry (reflected and refracted rays perpendicular) forces θt = 34.0°, and Snell’s law then yields n ≈ 1.482, matching 1.48.

Why other options are incorrect:
Options 1.40, 1.43, and 1.44 do not equal the Snell’s-law result 1.482 (they are significantly lower than the calculated value), so they are inconsistent with the given angles.

Final confirmation: The index of refraction of the material is 1.48.

A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material?单项选择题

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