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`

Explanation

The angle of incidence will be maximum for the ray travelling along the inner edge i.e. `theta`
If T.I.R. takes place for `theta`, all the rays will suffer T.I.R.
For T.I.R.
`thetageC`
`sinthetagesinC`
`(R)/((R+d))ge1/mu(=(1)/(3//2)=2/3)`
`3Rge(2R+2d)`
`Rge2d`
`dge2d`
`d/Rle1/2`
`(d/R)_(max)=1/2`