Is there a way to calculate the refracted and reflected rays? I know we use Snell's law to calculate the refracted rays, but is there a formula to calculate the angle of the reflected rays, or does it just follow the law of reflection? If so, is there a formula?
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According to the law of reflection for light rays, the incident ray angle is equal to the reflected ray angle (with respect to the normal to the interface). Snell's law relates the ratio of the sinuses of the angles and of incident and refracted ray, respectively, to the ratio of the refractive indices n2 and n1 of the media involved. Thus from a simple geometric drawing you obtain the formula for the angle between the reflected and the refracted ray as = 180°- - , where and are related by Snell's law.
When considering the reflection and refraction of polarized light beams, you have Fresnels formulae for the respective intensities. In particular, you'll see that you have no reflection of an in-plane polarized wave, when the reflected beam is at a right angle to the refracted beam. Thus only light with a linear polarization vertical to the incident plane is reflected. This happens when the incident angle is equal to the so-called Brewster angle.
On the other hand, when a light rays is incident on a medium with smaller refractive index, there will be transmission only for angles smaller than the critical angle for total reflection, which follows directly from Snell's law and the fact that the angle of the refracted ray cannot exceed 90° (sin = 1).
freecharly
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Both reflection and refraction can be explained using Snells Law:
Reflection $$n_1\sin\theta_i = n_2\sin\theta_r$$ where $\theta_r$ is the angle of reflection and $\theta_i$ is the angle of incidence.
Refraction $$n_1\sin\theta_i = n_2\sin\theta_t$$ where $\theta_t$ is the angle of transmission.
For reflection $n_1 = n_2$ so $\theta_i = \theta_r$
Stevan V. Saban
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