A glass slab consists of thin uniform layers of progressively decreasing refractive indices refractive index such that the refractive index of any layer is `mu-mDeltamu`. Here `mu and Deltamu` denotes the refractive index of 0th layer and the difference in refractive index betweeen any two consecutive layers, resepctively. The integer `m=0,1,2,3`... denotes the number of the suscessive layers. A ray of light from the 0th layers enters the 1st layer at an angle of incidence of `30^(@)`. After undergoing the mth refraction, the ray emerges paralllel to the interaface. If `mu=1.5 and Deltamu=0.15`, then the value of m is

Options

A. 20
B. 30
C. 40
D. 50

Answer

D

Explanation

By Snell's law
,u sin i=constant
`Rightarrow mu sin i=(mu-mDeltamu)sin r`
`"Where", mu=1.5,i=30^(@), r=90^(@), Deltamu=0.015 `
`1.5 sin 30 ^(@)=(1.5-m xx0.015) sin 90^(@)`
`(3)/(2)xx(1)/(2)=(1.5-mxx0.015)xx1`
`(3)/(4)-(3)/(2)=(-15m)/(1000)Rightarrow =((3)/(2)-(3)/4)xx1000`
`15m=(6-3)/(4)xx1000 Rightarrow m=(3)/(4)xx(1000)/(15)`
Magnification, `m=(3000)/(60)Rightarrow m=50`