Q50 / 57 · JEE Advanced 2021 (Paper 1) · Physics

A wide slab consisting of two media of refractive indices n1 and n2 is placed in air as shown in the figure. A ray of light is incident from medium n1 to n2 at an angle θ, where sinθ is slightly larger than 1n1. Take refractive index of air as 1. Which of the following statement(s) is (are) correct?

Figure

  • A
    The light ray enters air if n2=n1.
  • Correct answer
    B
    The light ray is finally reflected back into the medium of refractive index n1 if n2<n1.
  • Correct answer
    C
    The light ray is finally reflected back into the medium of refractive index n1 if n2>n1.
  • Correct answer
    D
    The light ray is reflected back into the medium of refractive index n1 if n2=1.

Solution

Figure

Option A: If n1=n2,

n1sinθ=n2sinθ1      ...1

and n2sinθ1=1×sinr     ...2

From (1) and (2),

sinr=n1sinθ

Now, sinθ>1n1, (given)

∴ sinr>1 (which is not possible)

and hence light will reflect back from air, n2 interface

Option B: If n2<n1,

Snell's law at A,

n1sinθ=n2sinθ1     ...3

Snell's law at B

n2sinθ1=sinr   ...(4)

From 3 and (4),

n1sinθ=sinr

∴  sinr>1 (not possible)

Hence, light might reflect from A or B.

Option C: If n2>n1,

n1sinθ=n2sinθ1       ...5 at A

n2sinθ=1×sinr       ...6 at B

∴  n1sinθ=1×sinr

∴sinr>1 (not possible)

∴ Light will reflect back into medium n1.

Option D: If n2=1,

n1sinθ=n2sinθ1

⇒sinθ1=n1sinθ

or sinθ1>1 not possible

Hence, light will reflect back into the medium.    

Hence, the correct answer is options: 'B', 'C', 'D'.

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