Chapter 11, Problem 64P

To determine

To Find: The angle of refraction.

Answer to Problem 64P

  $24.1°$

Explanation of Solution

Given Information:

The angle of incidence = $25°$

Cold air temperature= $-10°$ C

Warm air temperature= $+10°$ C

Formula used: According to Snell’s law

  $\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\mathrm{v}{1}_{}}{{\mathrm{v}}_2}$

Where, ${\mathrm{v}}_1$ and ${\mathrm{v}}_2$ are the velocities of the wave in the first and second medium.

Given that

  $\begin{array}{l}\mathrm{v}=331+0.6\mathrm{T}\\ {\mathrm{v}}_1=331+(0.6\times 10)=337\text{m/s}\\ {\mathrm{v}}_2=331+(0.6\times -10)=325\text{m/s}\end{array}$

Calculation:

  $\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\mathrm{v}{1}_{}}{{\mathrm{v}}_2}$

  $\begin{array}{l}\frac{\sin (25°)}{\sin \mathrm{r}}=\frac{337}{325}\\ \frac{0.423}{\sin \mathrm{r}}=\frac{337}{325}\\ \sin \mathrm{r}=\frac{0.423\times 325}{337}\\ \sin \mathrm{r}=0.408\\ \mathrm{r}=24.1°\end{array}$

Conclusion:

The angle of refraction is $24.1°$ .