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.

Explanation

Refraction at plane surface 1,
`mu=1,mu_2=(3)/(2),u=-mR,v=?`
`(mu_2)/(v)-(mu_1)/(u)=0`
`((3)/(2))/(v)-(1)/(-mR)=0impliesv=(-3)/(2)mR`
Refraction at spherical surface 2,
`mu_1=(3)/(2),mu_2=1,u=-((3)/(2)mR+R),R=-R,v=infty`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)`
`(1)/(infty)-((3)/(2))/(-((3)/(2)mR+R))=(1-(3)/(2))/(-R)`
`(1)/(mR+(2)/(3)R)=(1)/(2R)`
`m+(2)/(3)=2impliesm=2-(2)/(3)=(4)/(3)`