The path of a ray of light passing through an equilateral glass prism ABC is shown in figure. The ray of light is incident on face BC at the critical angle for just total internal reflection. The total internal reflection. The total angle of deviation after the refraction at face AC is `108^@`. Calculate the refractive index of the glass.

Explanation

In the figure shown,
`r_(2)=C`
`r_(1)=60-r_(2)=60-C`
`r_(3)=60-r_(2)=60-C`
`r_(1)=r_(3)=r` (say)
`i_(1)=i_(2)=i` (say)
Net deviation, `delta =(1-r)+(180-2r_(2))+(i-r)=108^(@)`
`r_(2)=r-i=36^(@)`
`C+60-C-i=36^@`
`i=24^@, sin24^@~~0.40`
Form Snell's law, we have
`sin24^@=musinr`
`0.4=musin(60^(@)-C)`
`0.4 = mu[(sqrt(3))/(2)cosC-(1)/(2mu)]`
`0.8=sqrt(3)musqrt(1-(1)/(mu^(2))-1)`
`:. mu^(2)-1=1.08`
`mu=1.447`