Question

A wide slab consisting of two media of refractive indices $n_{1}$ and $n_{2}$ is placed in air as shown in the figure. A ray of light is incident from medium $n _{1}$ to $n _{2}$ at an angle $\theta$, where $\sin \theta$ is slightly larger than $\frac1 { n _{1}}$. Take refractive index of air as $1$.Which of the following statement(s) is(are) correct?

• A. The light ray enters air if $n_{2}=n_{1}$
• B. The light ray is finally reflected back into the medium of refractive index $n _{1}$ if $n _{2}< n _{1}$
• C. The light ray is finally reflected back into the medium of refractive index $n_{1}$ if $n_{2}>n_{1}$
• D. The light ray is reflected back into the medium of refractive index $n_{1}$ if $n_{2}=1$

Answer 1

The Correct Option is B, C, D

\(\sin(\theta) > \frac{1}{n_1}\) … (i)

And \(n_1 \sin(\theta) = 1 \times \sin(r)\) … (ii)

\(⇒ sinr > 1\)

\(⇒\) refraction into air is not possible
Therefore correct options are :
(B) The light ray is finally reflected back into the medium of refractive index 𝑛₁ if \(n_2 < n_1\)
(C) The light ray is finally reflected back into the medium of refractive index 𝑛₁ if \(𝑛_2 > 𝑛_1 \)
(D) The light ray is reflected back into the medium of refractive index 𝑛1 if 𝑛₂ = 1