Question

A horizontal beam of light enters a 45

Answer 1

theta = incident angle = 45

r1 = refracted angle

using :: snells law :::   n*sin(r1) = sin(45)

                                         sin(r1) = 0.7/n

r2 = incident angle on vertical surface( second surface) .

then   r1 +r2 = 45

          r1 = 45-r2.

using snells law ::: nsin(r2) = sin30

                             n *sin( 45-r1) = 0.5

                            n [ sin(45)*cos(r1) - cos(45) *sin(r1) ] = 0.5

                            0.7n [cos(r1) - sin(r1) ] = 0.5

                              0.7n [ {(1-(0.7/n)² }^0.5 - 0.7/n] =0.5

                                  0.7n {(1-(0.7/n)² }^0.5    = 0.99

                                        {(n²- 0.49}^0.5   = 1.41

                                            n = 1.57