Chapter 14.5, Problem 56PPS

a.

To determine

To find: what is the angle of refraction.

Answer to Problem 56PPS

Angle of refraction $r\approx {13.71}^{\circ }.$

Explanation of Solution

Given information: The index of refraction of a diamond is 2.42 and the index of

refraction of air is 1.00. If a beam of light strikes a diamond at an angle of ${35}^{\circ }$

Formula used:

According to Snell’s Law $n_1\sin i=n_2\sin r$ , where $n_1$ is the index of the refraction of the medium the light is exiting, $n_2$ is the index of refraction of the medium the light is entering , i is the degree measure of the angle of incidence , and r is the degree measure of the angle of refraction.

Calculation:

Given the equation:

  $\begin{array}{c}{n}_1\sin i=n_2\sin r\\ n_1=1\\ i={35}^{\circ }\\ n_2=2.42\\ r=?\\ n_1\sin i=n_2\sin r\\ \sin r=\frac{n_1\sin i}{n_2}=\frac{1\times \sin {35}^{\circ }}{2.42}=\frac{0.57357644}{2.42}\approx 0.23701505785\\ r={\sin }^{-1}(0.23701505785)\approx {13.71}^{\circ }\\ r\approx {13.71}^{\circ }.\end{array}$

Therefore, angle of refraction is $r\approx {13.71}^{\circ }.$

b.

To determine

To explain: how a gemologist might use Snell’s Law to determine whether a diamond is genuine.

Answer to Problem 56PPS

Explanation of Solution

Given information:

Formula used:

According to Snell’s Law $n_1\sin i=n_2\sin r$ , where $n_1$ is the index of the refraction of the medium the light is exiting, $n_2$ is the index of refraction of the medium the light is entering , i is the degree measure of the angle of incidence , and r is the degree measure of the angle of refraction.

Calculation:

Given Snell’s Law is:

  $n_1\sin i=n_2\sin r$ .

To determine if a diamond is genuine, perform an experiment; note the angle of incident and the angle of refraction for a light beam striking the diamond, then determine the index of refraction for the piece of diamond and if get the value 2.42, then the diamond is genuine.