A light wave traveling in air impinges on an amber plate at an angle of incidence of 60º. If the angle of refraction is 34º, the velocity of light in amber must be approximately A) 0.52 × 10⁸ m/s. B) 4.64 × 10⁸ m/s. C) 1.86 × 10³ m/s. D) 2.09 × 10⁸ m/s. E) 4.64 × 10¹⁰m/s.

Question

Quizplus · Accepted Answer

The angle of incidence ($	heta_i$) and the angle of refraction ($	heta_r$) are related to the indices of refraction ($n_1$, $n_2$) and the velocity of light in each medium ($v_1$, $v_2$) by Snell's Law:

$$n_1\sin	heta_i = n_2\sin	heta_r$$

We can rearrange this to solve for the ratio of velocities:

$$\frac{v_1}{v_2} = \frac{n_2}{n_1} = \frac{\sin	heta_i}{\sin	heta_r}$$

Plugging in the given values:

$$\frac{v_{	ext{air}}}{v_{	ext{amber}}} = \frac{\sin 60^\circ}{\sin 34^\circ} \approx 2.09$$

Since the velocity of light in air is approximately $3	imes 10^8$ m/s, we can solve for the velocity of light in amber:

$$v_{	ext{amber}} = \frac{v_{	ext{air}}}{2.09} \approx \boxed{	extbf{(D)}\ 2.09	imes 10^8\ 	ext{m/s}}$$

A Light Wave Traveling in Air Impinges on an Amber