Example from Physics, 16.2 Refraction

Calculating Index of Refraction from Angles

Suppose you have an unknown, clear solid substance immersed in water and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.00°, and you observe the angle of refraction to be 40.30°. What are the index of refraction of the substance and its likely identity?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We must use the mathematical expression for the law of refraction to solve this problem because we are given angle data, not speed data.

$\frac{n_{1}}{n_{2}} = \frac{sin θ_{2}}{sin θ_{1}}$
16.10

The subscripts 1 and 2 refer to values for water and the unknown, respectively, where 1 represents the medium from which the light is coming and 2 is the new medium it is entering. We are given the angle values, and the table of indicies of refraction gives us n for water as 1.333. All we have to do before solving the problem is rearrange the equation

$n_{2} = \frac{n_{1} sin θ_{1}}{sin θ_{2}} .$
16.11
Solution
$n_{2} = \frac{(1.333) (0.7071)}{0.6468} = 1.457$
16.12

The best match from Table 16.2 is fused quartz, with n = 1.458.

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Strategy

Solution