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 $${\mu _2} > {\mu _3}$$

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $${2 \over 3}$$ times the wavelength in free space. The radius of the curved surface of the lens is