Question

The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If θc= 40.7° and a light ray strikes this material (from air) at an angle of 34.8° with respect to the normal of the surface. Calculate the angle of the reflected ray (in degrees). FYI n = 1.533

Answer 1

Given

whne the solid is in air

   the critical angle is when the light ray enters from denser medium to rarer medium, the angle of incedence, where the refracted ray just grazes the boundary between two surfaces so that the angle of refraction becomes 90 degrees

HERE the critcal angle is 40.7 degrees

From Snell's law na sin theta A = nb sin theta B

       na sin 40.7 = 1*sin90

       na= 1/ sin (40.7)

       na = 1.533

when light ray strikes the surface from air , the angle of incidence is 34.8 degrees,

the angle of recraction is given by sin theta B = na/nb*sin theta A

               sin theta B = 1/1.533 sin (34.8) = 0.3722854322795

                   theta B = arc sin (0.3722854322795)
                   theta B = 21.86 degrees

and the angle of reflection = angle of incidence that is = 34.8 degrees