1.

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:

Answer»

`{:(P,Q,R,S),(2,3,1,4):}`
`{:(P,Q,R,S),(1,2,4,3):}`
`{:(P,Q,R,S),(4,1,2,3):}`
`{:(P,Q,R,S),(2,3,4,1):}`

Solution :For PATH e - f, angle in medium `mu_(2)`, is less hence `mu_(2)gtmu_(1)`. Moreover, angle in medium `mu_(3)`is ALSO increasing hence `mu_(3)ltmu_(2)`. Hence P can be MATCHED with 2.
For path e-g, there is no deviation while emerging from prism, hence `mu_(1)=mu_(2)`. Hence Q can be matched with 3.
For path e-h, angle in medium `mu_(2)` is greater than in `mu_(1)` and hence `mu_(2)ltmu_(1)`. Moreover, there is no internal reflection so `mu_(2)ltsqrt(2)` `mu_(2), mu_(2)gtmu_(3)`is also correct according to RAY DIAGRAM. Hence R can be matched with 4.
For path e-i there is total internal reflection taking place and hence `mu_(1)gtsqrt(2)``mu_(2)`. Hence S can be matched with 1.
`P-2, Q-3, R-4, S-1` is correct.
Hence, option (d) is correct.


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