A ray of light falls on a transparent sphere with centre at C as shown in figure. The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is

Options

A. `mu=sqrt(2)`
B. `mu=sqrt((3)/(2))`
C. `mu=sqrt(3)`
D. `mu=sqrt((5)/(2))`

Answer

A

Explanation

Apply Snell.s law at points A abd B
`1sin60^(@)=musinr` …(i)
`musinr=1sinphi` ...(ii)
Solving equations (i) and (ii), we get `phi=60^(@)`
Also, `2r+180^(@)-phi=180^(@)`
`2r+180^(@)-60^(@)=180^(@)`
or `2r=60^(@)` or `r=30^(@)`
From equation (i), we get `mu=(sin60^(@))/(sinr)=(sin60^(@))/(sin30^(@))=sqrt(3)`