A beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of 40° with the normal, and the refracted beam makes an angle of 26° with the normal. What is the speed of light in the transparent material? (c = 3.0 × 108 m/s, The refractive index of air , nair = 1)

Question

A beam of light traveling in air strikes a slab of transparent material.  The incident beam makes an angle of 40° with the normal, and the refracted beam makes an angle of 26° with the normal.  What is the speed of light in the transparent material? (c = 3.0 × 108 m/s, The refractive index of air , nair = 1)

BlackTom AI · Accepted Answer

To analyze the problem, recall that light slows down when entering a medium and slows according to the refractive index via Snell's law: n1 sin(theta1) = n2 sin(theta2).

Option by option evaluation:
- Option: 1.0 × 10^8 m/s
  This would imply a refractive index n2 = c/v ≈ (3.0×10^8)/(1.0×10^8) = 3.0, which is much larger than the typical refractive index for transparent materials at optical wavelengths. Given theta1 = 40° and theta2 = 26°, Snell's law yields n2 ≈ sin(40°)/sin(26°) ≈ 0.6428/0.4384 ≈ 1.47, not 3.0. So this option is incorrect.
- Option: 3.0 × 10^8 m/s
  This equals the speed of light in vacuum, which would correspond to n2 = 1.0. But the measured refraction angles (40° and 26°) show the light actually enters a slower medium than air (n2 > 1). Therefore this option is incorrect.
- Option: 2.0 × 10^8 m/s
  This gives an approximate refractive index n2 ≈ c/v ≈ (3.0×10^8)/(2.0×10^8) = 1.5. This is very close to the n2 value from Snell's law, which is about 1.47, so this option is consistent with the given angles and is a plausible correct choice.
- Option: 2.3 × 10^8 m/s
  This would correspond to n2 ≈ 3.0×10^8 / 2.3×10^8 ≈ 1.304, which is lower than the 1.47 obtained from Snell's law with the given angles. Since Snell's law requires n2 ≈ 1.47, this option does not fit the data.
- Option: 0.50 × 10^8 m/s
  This would imply n2 ≈ 6, which is far outside typical transparent materials and would not satisfy Snell's law for theta1 = 40° and theta2 = 26°. This option is clearly incorrect.

Putting the pieces together, the speed of light in the material is close to 2.0 × 10^8 m/s, yielding a consistent refractive index around 1.47, which matches the observed refraction angles.

PHYSICS 1201 SU2025 (10585) MT2 Exam- Requires Respondus LockDown Browser

查看解析

登录即可查看完整答案

类似问题

Question at position 1 Given the figure below where light travels from one medium to another, and with Snell's Law in mind as well as the difference between the angles apparent; what is the relationship between the refractive indices n_1 and n_2? n_1 > n_2n_1 < n_2n_1 = n_2Not enough information

A light ray passes from water (refractive index ( n1 = 1.33 )) into diamond (refractive index ( n2 = 2.42 )). If the angle of incidence in water is ( 300 ), what is the angle of refraction in diamond?

Which of the following statements best describes Snell's Law and its application in determining the path of light as it passes from one medium to another?

A thin beam of light enters a thick plastic sheet from air at an angle of 32.0° with the normal and continues in the sheet at an angle of 23.0° with the normal. What is the index of refraction of the plastic? The index of refraction of the air, nair = 1.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单