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 relationship between `mu_(1) , mu_(2) "and" mu_(3)` , it takes one of the four possible paths 'ef' , 'eg' , 'eh' or 'ef'

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 rarr f , 1. mu_(1)gt sqrt(2mu_(2))) , ( Q. e rarr g , 2. mu_(2) gt mu_(1) "and" mu_(2) gt mu_(3)), ( R. e rarr f , 3. mu_(1) = mu_(2)), ( S. e rarr f , 4. mu_(2) lt mu_(1) lt sqrt(2mu_(2)) "and" mu_(2) gt mu_(3)):}`
Codes :
`{:( P , Q , R , S) , ((A) 2 , 3 , 1 , 4), ((B) 1 , 2 , 4 , 3) , ((C) 4 , 1 , 2 , 3) , ((D) 2, 3 , 4 , 1):}`

Answer

D

Explanation

(P) at prism surface ray moving towards normal so `(mu_(2) gt mu_(1))` at block surface ray moving away from normal so `(mu_(3) - mu_(2))`
(Q) No deflection of ray on both surface , so `mu_(1) = mu_(2) = mu_(3)`
(R) at prism surface ray moving away from normal so `mu_(2) lt mu_(1) `. At block surface ray moving away from normal so `mu_(3) lt mu_(2)` but since on total internal reflection not takes place on prism surface `mu_(1) "sin" 45^(@) gt mu_(2) "sin" 90^(@) implies mu_(1) gt sqrt(2) mu_(2)`
(S) Total internal reflection takes place so `mu_(1) "sin"45^(@) lt mu_(2) "sin"90^(@) implies mu_(1)gt sqrt(2) mu_(2)`