Question

Choose the correct answer:
A ray of light passes from air into water, striking the surface of
the water with an angle of incidence of 45'. Which of the
following four quantities change
as the light enters the water? [1] Wavelength, [I1] frequency,
[III] speed of propagation, [IV] direction of propagation.
(a) I and II only. (d) III and IV only.
(b) II, III, and IV only. (e) I, II, III, and IV. (c) I, III, and IV only.

Answer 1

Let's write the Snell's Law (or the Law of Refraction):

$$n_isin\theta_i=n_rsin\theta_r,$$ $$\dfrac{sin\theta_i}{sin\theta_r}=\dfrac{v_i}{v_r}=\dfrac{n_r}{n_i},$$

here, $\theta_i$ is the angle of incidence, $\theta_r$ is the angle of refraction, $n_i$ is the index of refraction of the air, $n_r$ is the index of refraction of the water, $v_i$ is the speed of light in the air, $v_r$ is the speed of light in the water.

As we can see from the Snell's Law, the direction of propagation of the ray of light is change. Also, the speed of propagation of the ray of light in water will decrease. Finally, there is the speed wave formula that relates the speed of propagation of the ray of light and the wavelength:

$$v=f \lambda$$

As we can see from the formula, if the speed of propagation of the ray of light change, then the wavelength also change. Therefore, only the frequency remains unchanged. Thus, the correct answer: c) I, III, and IV only.

Answer:

c) I, III, and IV only