Answer to Question #156728 in Physics for Festus

Question

The wave length and a set of wave travelling in a medium are 60cm and 320cm² means a plane refraction surface at an angle of 60°.If velocity after is 280cm², calculate the wave length of the wave in the second medium and also the angle of refraction.

Answer 1

Find the refractive index:

$$n=\frac{v_i}{v_r}=\frac{320}{280}=1.14.$$

The angle of refraction can be found from Snell's law:

$$n=\frac{\text{ sin}\theta_i}{\text{ sin}\theta_r},\\\space\\ \theta_r=\text{arcsin}\frac{\text{ sin}\theta_i}{n}=\text{arcsin}\frac{\text{ sin}60°}{1.14}=49.4°.$$

The length of refracted wave is

$$\lambda_r=\frac{\lambda_i}{n}=\frac{60}{1.14}=52.6\text{ cm}.$$