# Problem: A light ray in air is incident on a transparent material whose index of refraction is n.a. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence.b. Evaluate your expression for light incident on glass.

###### FREE Expert Solution

Snell's law:

$\overline{){{\mathbf{\eta }}}_{{\mathbf{1}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta }}}_{{\mathbf{1}}}{\mathbf{=}}{{\mathbf{\eta }}}_{{\mathbf{2}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta }}}_{{\mathbf{2}}}}$, where η1 is the refractive index of the first medium, η2 is the refractive index of the second medium, θ1 is the angle of incidence, and θ2 is the angle of refraction.

(a)

in our case, the first medium is air.

Therefore, η1 = 1

We're told that the angle of refraction is equal to half the angle of incidence.

82% (253 ratings) ###### Problem Details

A light ray in air is incident on a transparent material whose index of refraction is n.
a. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence.
b. Evaluate your expression for light incident on glass.

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