Question

A beam of light in air strikes a piece of glass (n = 1.61) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.

Answer 1

Law of reflection is angle of incidence = angle ofreflection

i.e., angle of reflection   = i   ---(1)

in given problem angle of reflection =2(  angle of refraction )

                                                    i = 2 r    from eq ( 1)

from snell's Law , index of refraction n = sin i / sinr

                                                    1.61 = sin 2 r / sin r

                                                            = 2 sin r cos r / sin r

                                                             =2 cos r

                                                    cos r = 1.61 / 2

                                                             = 0.805

                                                           r = 36.38 ^o

So , angle of incidence i = 2 r

                                    = 72.77 ^o