A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refractive index n = $$\sqrt 2 $$. Light undergoes total internal reflection in the prism at the face PR when a has a minimum value of 45°. The angle q of the prism is :

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the below figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

A right-angled prism of refractive index $$\mu$$₁ is placed in a rectangular block of refractive index $$\mu$$₂, which is surrounded by a medium of refractive index $$\mu$$₃, as shown in the figure. A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between $$\mu$$₁, $$\mu$$₂ and $$\mu$$₃, 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
P.	$$e \to f$$	1.	$${\mu _1} > \sqrt 2 {\mu _2}$$
Q.	$$e \to g$$	2.	$${\mu _2} > {\mu _1}$$ and $${\mu _2} > {\mu _3}$$
R.	$$e \to h$$	3.	$${\mu _1} = {\mu _2}$$
S.	$$e \to i$$	4.	$${\mu _2} < {\mu _1} < \sqrt 2 {\mu _2}$$ and $${\mu _2} > {\mu _3}$$