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 mR from it. Find the value of m for whicha ray from P will emerge parallel to the table as shown in the figure.

Answer

`m=4//3`

Explanation

Taking Refraction from curved surface
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`(1)/(oo)-(1.5)/(u)=(1-1.5)/(-R )`
`-(3)/(2u)=(1)/(2R )`
`u=-3R`
The must be the image of`P` due to refraction from plane surface.
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(oo)`
`(1.5)/(-2R)-(1)/(-mR)=0`
`(1)/(mR)=(3)/(4R)`
`m=(4)/(3)`