Question

Q1.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

Step-by-step explanation:

Answer:

The value of refractive index of a medium, when the critical angle is given, can be found out by the formula:

$\boxed{ n = \dfrac{1}{Sin\: \theta_{c}}} </p><p>$

Here, n refers to the refractive index and \theta_{c}θ

c

refers to the critical angle.

According to the question, \theta_{c}θ

c

= 30°. Hence substituting in the formula we get:

$\begin{gathered}\rightarrow n = \dfrac{1}{Sin\:30^{\circ}}\\\\\rightarrow n = \dfrac{1}{0.5}\\\\\rightarrow \boxed{n = 2}\end{gathered}$

Hence the refractive index is 2.

We know that.

$\boxed{ Refractive\:Index = \dfrac{ c }{ v }} </p><p>$

Where c is the speed of light and v is the speed of light in the medium.

Substituting the known values we get:

$\begin{gathered}\rightarrow 2 = \dfrac{3 \times 10^8}{v}\\\\\rightarrow v = \dfrac{3 \times 10^8}{2}\\\\\rightarrow \boxed{v = 1.5 \times 10^8\:\:m/s}\end{gathered}$

Hence the speed of light in that medium is 1.5 × 10⁸ m/s.