Question

The value of critical angle is 30° for total internal
reflection from any medium to vacuum; the speed of light
in that medium.
​

Answer 1

Answer:

In the medium, "speed of light" is 1.5 \times 10^8 \ m/s1.5×10

8

m/s

Explanation:

According to Snell's law, the ratio of sin I (sine of angle of incidence) and sin R (sine of angle of refraction) is equal to the ratio of v1 (velocity of light in medium 1) and v2 (velocity of light in medium 2). It is also equal to the reciprocal of the ratio of n1 ("refractive index" of medium 1) and n2 ("refractive index" of medium 2)

As the incident angle is always 90°;

Thus,

\frac{n 1}{n 2}=\frac{\sin I}{\sin R}

n2

n1

=

sinR

sinI

\frac{n 1}{n 2}=\frac{\sin 90}{\sin 30}

n2

n1

=

sin30

sin90

\therefore \frac{n 1}{n 2}=2∴

n2

n1

=2

We also know that,

\frac{n 1}{n 2} = \frac{v 2}{v 1}

n2

n1

=

v1

v2

So,

\frac{3 \times 10^{8}}{v 1}=2

v1

3×10

8

=2

\therefore v 1=\frac{3 \times 10^{8}}{2}∴v1=

2

3×10

8

v 1=1.5 \times 10^{8} \ \mathrm{m} / \mathrm{s}v1=1.5×10

8

m/s