A right-angled prism of refractive index μ 1 is placed in a rectangular block of refractive index &#956…

A right-angled prism of refractive index μ 1 is placed in a rectangular block of refractive index μ 2 , which is surrounded by a medium of refractive index μ 3 , as shown in the figure. A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between μ1, μ2 and μ3, it takes one of the four possible paths ef, eg, eh or ei.

Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:
  List I   List II
A. e→f P. μ 1 > 2 μ 2
B. e→g Q. μ 2 > μ 1  and  μ 2 > μ 3
C. e→h R. μ 1 = μ 2
D. e→i S. μ 2 < μ 1 < 2 μ 2  and  μ 2 > μ 3

 

  1. a-s;b-r;c-p;d-q;
  2. a-q;b-s;c-r;d-p;
  3. a-q;b-r;c-s;d-p;
  4. a-s;b-r;c-p;d-q;

Solution

For e→i,  4 5 ∘ > θ c
sin  4 5 ∘ > sin  θ c
1 2 > μ 2 μ 1
μ 1 > 2 μ 2
For e→f, an angle of refraction is lesser than the angle of incidence. So, μ 2 > μ 1 and then μ 2 > μ 3 .
For e→g, μ1=μ2.
For e→h, μ2<μ1<2μ2 and μ2>μ3. !

Asked in: JEE Advanced 2013 (Paper 2)

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