Q36 / 51 · JEE Advanced 2023 (Paper 1) · Physics

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is δ=60o (see Figure-1). The angle of minimum deviation for red light from the same prism is δmin=30o (see Figure-2). The refractive index of the prism material for blue light is 3. Which of the following statement(s) is(are) correct?

Figure

  • Correct answer
    A
    The blue light is polarized in the plane of incidence
  • B
    The angle of the prism is 45o
  • Correct answer
    C
    The refractive index of the material of the prism for red light is 2
  • Correct answer
    D
    The angle of refraction for blue light in air at the exit plane of the prism is 60o

Solution

For no reflection:

Figure

tani=3

⇒i=60°

Applying Snell's law at left interface, we get

⇒1×sini=3×sinr1⇒sinr1=12⇒r1=30o

Now, for given values

δ=i+e-A⇒60°=60°+e-A⇒e=A

Then, 

A=r1+r2⇒r2=A-r1=30o

For red light:

Expression to find minimum deviation is given by,

μ=sinA+δm2sinA2=sin60°+30°2sin60°2=1212=2

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

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