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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$\begingroup$ Related 01 : Snell's law in vector form. $\endgroup$– FrobeniusCommented Apr 12 at 3:30
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$\begingroup$ Related 02 : Why one should follow Snell's law for shortest time?. $\endgroup$– FrobeniusCommented Apr 12 at 3:31
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$\begingroup$ Related 03 : How can we express Snell's law as.... $\endgroup$– FrobeniusCommented Apr 12 at 3:33
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1$\begingroup$ Law of reflection states that reflection angle is same as incident angle to the normal. $\endgroup$– Agnius VasiliauskasCommented Apr 12 at 6:16
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2 Answers
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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 $\theta_i = \theta_r$
answered Apr 12 at 19:59
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$\begingroup$ Thank you for the explanation, but can't the index of refraction be different in reflection? Like if light reflects from water from air, doesn't that mean that n1 does not equal n1? $\endgroup$– AstrovisCommented Apr 12 at 21:45
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1$\begingroup$ @Astrovis the light is reflected from the interface between the two media and never enters the second medium. The reflected light travels only in one medium so n1 = n2 $\endgroup$ Commented Apr 13 at 0:00
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$\begingroup$ Ah ok, so saying n1 = n2 is an approximation that can be used in reflection, since the refractive indices don't matter. $\endgroup$– AstrovisCommented Apr 13 at 3:45
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According to the law of reflection for light rays, the incident ray angle 𝛂 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 𝛂 and 𝛃 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 𝛄 between the reflected and the refracted ray as 𝛄 = 180°- 𝛂 - 𝛃, where 𝛂 and 𝛃 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 𝛃 of the refracted ray cannot exceed 90° (sin 𝛃 = 1).
