91Ó°ÊÓ

Speed of deep water is$v_d=4.0 \text{m/s}$.

Speed of shallow water is$v_s=3.0 \text{m/s}$ .

All three rays—the incident, normal at the point of incidence, and refracted—lie in the same plane. According to the law of refraction, this is the case.

${\mathbf{n}}_{\mathbf{1}}{\mathbf{²õ¾\pm ²Ôθ}}_{\mathbf{1}}\mathbf{=}{\mathbf{n}}_{\mathbf{2}}{\mathbf{²õ¾\pm ²Ôθ}}_{\mathbf{2}}$

Here, $n_1$is refractive index in rarer medium, $n_2$is refractive index in denser medium.

Apply the law of refraction,

$\frac{\sin {\mathrm{θ}}_2}{\sin {\mathrm{θ}}_1}=\frac{v_s}{v_d}$

Substitute all the value in the above equation.

Consequently solve as follows:

$$\begin{gathered} {\mathrm{θ}}_2={\sin }^{-1}\left(\frac{v_s\sin 30°}{v_d}\right) \\ ={\sin }^{-1}\left(\frac{3.0 \text{m/s}×\sin 30°}{4.0 \text{m/s}}\right) \\ =22° \end{gathered}$$

Hence, the angle between direction of motion and the normal is$22°$ .

Refraction causes the angle of incidence to steadily decrease, as demonstrated in the math above (from 30° to 22°). After multiple refractions${\mathrm{θ}}_2$ ,will eventually approach zero. Because of this, most waves arrive at a shore normally.