Find the angle of incidence if the angle of reflection is twice the angle of refraction.?

Question

A beam of light in air strikes a slab of crown glass (n=1.52) and is partially reflected and partially refracted.

Answer 1

with the snell's law
n1sin i=n2sin r
here n1 refracting index of air=1
n2 refracting index of glass =1,52

i angle of incidence
r angle of refraction

but we have that angle of incidence = angle of reflexion and we have that the angle of reflexion is x 2 the angle of refraction.That means that the angle of incidence is equal to 2r
then we have 1 sin2r=1.52 sin r

if we rearrange 1/1.52=sin r/sin 2r

we cannot simplify unless we change sin 2r

sin2r=2 sinr cosr

then 1/1.52=sinr/2 sinr cosr

cosr= 1.52/2=.76

r= 41
then i=82

hope my calculus are good, you should verify

P.A.

Answer 2

Hi. You can use Snell's Law http://www.answers.com/topic/snell-s-law-2 and refractive index http://www.answers.com/topic/refractive-index I would start with a 45 deg angle of incidence to determine the angles empirically.