A ray of light incident on the horizontal surface of glass slab at `70^(@)` just grazes the adjacent vertical surface after refraction. Compute the critical angle and refractive index.

Explanation

Let AB is incident ray and BC is refracted ray through glass slab.
Then `r+C+90^(@)=180^(@)`
r + C = 90
r = 90 - C
From `mu=1/(sinC)=1/sin(90^(@)-r)=1/cosr`
From `sinr=sqrt(1-cos^(2)r)=sqrt(1-(1/mu)^(2))=(sqrt(mu^(2)-1))/mu`
By Snell.s law `mu=sini/sinr`
`sini=musinr=(musqrt(mu^(2)-1))/mu`
`sini=sqrt(mu^(2)-1)ormu=sqrt(1+sin^(2)70^(@))`
`mu=sqrt(1+(0.9397)^(2))=1.372`
`sinC=1/mu=0.7289rArrC=46^(@)47.`