The angle that exists between the light that is reflected and the ray that is refracted is mathematically given as
=122.2°
What is Snell's Law?
When talking about light or other waves that have to cross a border between two isotropic mediums like water, glass, or air, Snell's law is the formula used to define the connection between the angles of incidence and refraction.
Use the following Snell's law equation.
[tex]$n_{1} \sin \theta_{i}=n_{2} \sin \theta$[/tex]
Rearrange the above equation for the refractive angle of the refracted ray in zircon.
[tex]$\begin{aligned}\sin \theta_{r} &=\frac{n_{1} \sin \theta_{i}}{n_{2}} \\\theta_{r} &=\sin ^{-1}\left(\frac{n_{1} \sin \theta_{i}}{n_{2}}\right) \\&=\sin ^{-1}\left(\frac{(1) \sin 39^{\circ}}{1.95}\right) \\&=\sin ^{-1}\left(\frac{(1)(0.629320)}{1.95}\right) \\&=18.83^{\circ}\end{aligned}$[/tex]
The angle between the part of the reflected ray and the refracted beams is,
[tex]$\begin{aligned}\phi &=180^{\circ}-\left(\theta_{i}+\theta_{r}\right) \\&=180^{\circ}-\left(39^{\circ}+18.83^{\circ}\right) \\&=122.2^{\circ}\end{aligned}$[/tex]
In conclusion, the angle that exists between the light that is reflected and the ray that is refracted is
=122.2°
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