Chapter 18, Problem 10STP

To determine

The angle of refraction.

Answer to Problem 10STP

  $55.86°$

Explanation of Solution

Given:

Angle of incidence, $i=20.0°$

Critical angle for diamond-air interface, $i_c=24.4°$

Formula used:

According to Snell’s law:

  $\frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_1}$

Here, i the angle of incidence, r is the angle of refraction and $\mu$ refers to the refractive index.

Calculations:

As the angle of incidence is less than the critical angle, total internal reflection will not occur.

Refractive index of diamond is: ${\mu }_1=2.42$

Refractive index of air is: ${\mu }_2=1.0$

Angle of refraction can be calculated as follows:

  $\begin{array}{c}r={\sin }^{-1}\left(\frac{{\mu }_1\sin i}{{\mu }_2}\right)\\ ={\sin }^{-1}\left(\frac{2.42\times \sin 20.0°}{1.0}\right)\\ =55.86°\end{array}$

Conclusion:

Thus, the angle of refraction is $55.86°$ .