optics problemsssssss

1 a parallel beam of light falls on a quarter cylinder of radius R as shown in fig. (A) μ=√3 . max. value of OP as shown in fig. (B) ,so that rays do not suffer total internal reflection at the curved surface is

2.right face of a glass cube is silvered as shown. a ray of light is incident on the surface as shown ,find the deviation of the ray when it comes out of the glaa cube
angle shown in fig. is 45^.


3.a hemisphere (μ=3) of radius placed on a horizontal surface with its base touching the surface .A vertical beam of cross sectional radius (√3/2)r is incident symmetrically on its curved surface.find radius of the spot of light formed on the horizontal surface