Chapter 7.3, Problem 112AYU

To determine

Determine the angle of refraction.

Answer to Problem 112AYU

  $\boxed{\theta =27}$ Degrees.

Explanation of Solution

Given information:

The following discussion of Snell’s Law of Refraction is needed for problems. Light, sound, and other waves travel at different speeds, depending on the media (air, water, wood, and so on) through which they pass. Suppose that light travels from a point A in one medium, where its speed is $v_1$ , to a point B in another medium, where its speed is $v_2$ . Refer to the figure, where the angle ${\theta }_1$ is called the angle of incidence and the angle ${\theta }_2$ is the angle of refraction. Snell’s Law, which can be proved, using calculus, states that

  $\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}$

The ratio $\frac{v_1}{v_2}$ is called the index of refraction. Some values are given in the table shown to the right.

  

The index of refraction of light in passing from a vacuum into dense flint glass is $1.66$ . If the angle of incidence is $50°$ , determine the angle of refraction.

Calculation:

Let us consider the following figure

Let us consider the following expression

  $\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}\mathrm{.....}(1)$

Where ${\theta }_1$ is the angle of incidence and ${\theta }_2$ is the angle of refraction

  $\frac{v_1}{v_2}$ is the index of refraction

The index of refraction of light in passing from vacuum into dense glass is given as

  $\frac{v_1}{v_2}=1.66$

Here, ${\theta }_1=50$ then from equation (1)

  $\frac{\sin 50}{\sin {\theta }_2}=1.66$

  $\sin {\theta }_2=\frac{\sin 50}{1.66}$

  $\sin {\theta }_2=\frac{0.766}{1.66}$

  $\sin {\theta }_2=0.46$

Hence,

  ${\theta }_2={\sin }^{-1}(0.46)$

  ${\theta }_2\approx 27$

Hence, we conclude that

  $\boxed{\theta =27}$ Degrees.