A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point object P is kept at a distance of m R from it as shown in figure. For what value of m for which a ray from P will emerge parallel to the table?

Step-by-step solution

Refraction at plane surface (1), n₁=1, n₂=1.5= 3 2 , u=-m R, v=? Using formula, n₂ v - n₁ u = n₂-n₁ R aligned & R= for plane surface. & 3 / 2 v - 1 (-m R) =0 & v=- 3 2 m R aligned Refraction at spherical surface (2) aligned & u=- ( 3 2 m R+R ) and R=-R, v= , & n₁= 3 2 , n₂=1 aligned 1 - 3 / 2 [- ( 3 2 m R+R ) ] = 1-3 / 2 -R aligned & 3 / 2 R(3 m+2) 2 = 1 / 2 R & 6 3 m+2 =1 3 m+2=6 & m= 4 3 & aligned