A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4. If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?

Question

A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4.  If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?

BlackTom AI · Accepted Answer

We start by restating the given scenario and known quantities in the problem. A ray passes from medium 1 into medium 2. The angle of incidence in medium 1 is 31 degrees, and the refracted angle in medium 2 is 24.4 degrees. The speed of light in medium 2 is 1.76 x 10^8 m/s. We are to find the index of refraction of medium 1.

First, determine the refractive index of medium 2 using the relationship n = c / v, where c is the speed of light in vacuum (~3.00 x 10^8 m/s). So n2 = (3.00 x 10^8) / (1.76 x 10^8) ≈ 1.7045.

Next, apply Snell's law at the interface: n1 sin(theta1) = n2 sin(theta2), where theta1 is the angle of incidence (31°) and theta2 is the angle of refraction (24.4°).

Solve for n1: n1 = n2 sin(theta2) / sin(theta1).

Compute the sines: sin(24.4°) ≈ 0.414 and sin(31°) ≈ 0.515.

Plug in the values: n1 ≈ 1.7045 * (0.414 / 0.515).

Calculate the ratio 0.414 / 0.515 ≈ 0.804, and multiply by 1.7045 to get n1 ≈ 1.37.

Therefore, the index of refraction of medium 1 is approximately 1.37.

Note on units and consistency: the result uses standard electromagnetic relations and consistent use of c for vacuum light speed, and the given speeds, angles, and resultant n1 are all dimensionally coherent. A small rounding difference in sine values would still yield a value near 1.37.

A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4. If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?简答题

类似问题

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?

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?

The angle of incidence

A ray of light, which is traveling in air, is incident on a glass plate at a 45° angle. The angle of refraction in the glass

Light exits a diamond (n = 2.42) into air. The angle of incidence is 15.0°. What is the angle of refraction?

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?

更多留学生实用工具

智能学习助手

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