Question 144: Ray Optics

Question

The critical angle for a denser-rarer interface is $$45^{\circ}$$. The speed of light in rarer medium is $$3 	imes 10^{8} \mathrm{~m} / \mathrm{s}$$. The speed of light in the denser medium is:

Accepted Answer

To find the speed of light in the denser medium, we can use Snell's Law at the critical angle, where the angle of refraction is $$90^{\circ}$$. Snell's Law states:
$$n_1 \sin{	heta_1} = n_2 \sin{	heta_2}$$
where $$n_1$$ and $$n_2$$ are the indices of refraction for the denser and rarer media, respectively, and $$	heta_1$$ and $$	heta_2$$ are the angles of incidence and refraction, respectively.
In this case, we have:
$$n_1 \sin{45^{\circ}} = n_2 \sin{90^{\circ}}$$
The critical angle is given as $$45^{\circ}$$, and the speed of light in the rarer medium is given as $$3 	imes 10^8 \mathrm{~m/s}$$. We can find the index of refraction of the rarer medium using the formula:
$$n = \frac{c}{v}$$
where $$c$$ is the speed of light in a vacuum ($$3 	imes 10^8 \mathrm{~m/s}$$), and $$v$$ is the speed of light in the medium.
For the rarer medium, we have:
$$n_2 = \frac{3 	imes 10^8 \mathrm{~m/s}}{3 	imes 10^8 \mathrm{~m/s}} = 1$$
Now we can rewrite Snell's Law as:
$$n_1 \sin{45^{\circ}} = 1 \cdot 1$$
$$n_1 \sin{45^{\circ}} = 1$$
$$n_1 = \frac{1}{\sin{45^{\circ}}}$$
Since $$\sin{45^{\circ}} = \frac{1}{\sqrt{2}}$$, we have:
$$n_1 = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}$$
Now, we can find the speed of light in the denser medium using the formula for the index of refraction:
$$v_1 = \frac{c}{n_1}$$
$$v_1 = \frac{3 	imes 10^8 \mathrm{~m/s}}{\sqrt{2}}$$
$$v_1 = 2.12 	imes 10^8 \mathrm{~m/s}$$
So, the speed of light in the denser medium is $$2.12 	imes 10^8 \mathrm{~m/s}$$.

Answer

$$2 .12 	imes 10^{8} \mathrm{~m} / \mathrm{s}$$

Answer

$$5 	imes 10^{7} \mathrm{~m} / \mathrm{s}$$

Answer

$$\sqrt{2} 	imes 10^{8} \mathrm{~m} / \mathrm{s}$$

Answer

$$3.12 	imes 10^{7} \mathrm{~m} / \mathrm{s}$$

Ray Optics

The critical angle for a denser-rarer interface is $45^{\circ}. The speed of light in rarer medium is 3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. The speed of light in the denser medium is:

Choose the correct answer: