Question

A glass rod having square cross-section is bent into the shape as shown in the figure. The radius of the inner semi-circle is R and width of the rod is d. Find the minimum value of `d//R` so that the light that enters at A will emerge at B. Refractive index of glass is `mu=1.5`

Answer 1

Consider the figure. If smallest angle of incidence `theta` is greater than critical angle then all light will emerge out at B.
`rArr thetagesin^(-1)(1/(mu))rArr sinthetage1/(mu)`
From figure, `sintheta=R/(R+d)`
`rArrR/(R+d)ge 1/(mu)rArr(1+d/R)lemu`
`rArr d/Rlemu-1rArr(d/R)_(max)=0.5`