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 $θ$ , where $\sin θ$ is slightly larger than $\frac{1}{n_{1}} .$ Take refractive index of air as 1. Which of the following statement(s) is(are) correct [2021]

Question

Smart Achievers · Accepted Answer

(2, 3, 4)

Given, $\sin θ_{1} > \frac{1}{n_{1}}$

$n_{1} \sin θ_{1} > 1$

Let us draw the ray diagram

So, by Snell's law,

$n_{1} \sin θ_{1} = n_{2} \sin r = 1 \times \sin r'$

$\Rightarrow \sin r' = n_{1} \sin θ_{1}$

As $n_{1} \sin θ_{1} > 1$ $\Rightarrow \sin r' > 1,$ which is impossible.

Therefore, $r'$ does not exist, i.e., light will never enter the air.

So, light will always be reflected back into medium 1 whatever is the value of $n_{1}$ and $n_{2}$ .

Hence, options (2), (3), (4) are correct.

Solution

1 The light ray enters air if $n_{2} = n_{1}$

2 The light ray is finally reflected back into the medium of refractive index $n_{1}$ , if $n_{2} < n_{1}$

3 The light ray is finally reflected back into the medium of refractive index $n_{1}$ , if $n_{2} > n_{1}$

4 The light ray is reflected back into the medium of refractive index $n_{1}$ , if $n_{2} = 1$

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Solution

1 The light ray enters air if n2=n1

2 The light ray is finally reflected back into the medium of refractive index n1, if n2<n1

3 The light ray is finally reflected back into the medium of refractive index n1, if n2>n1

4 The light ray is reflected back into the medium of refractive index n1, if n2=1

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1 The light ray enters air if $n_{2} = n_{1}$

2 The light ray is finally reflected back into the medium of refractive index $n_{1}$ , if $n_{2} < n_{1}$

3 The light ray is finally reflected back into the medium of refractive index $n_{1}$ , if $n_{2} > n_{1}$

4 The light ray is reflected back into the medium of refractive index $n_{1}$ , if $n_{2} = 1$