A beam of light both reflects and refracts at the surface...

A beam of light both reflects and refracts at the surface between air and glass as shown in Figure P34.23. If the refractive index of the glass is $n_{g^{\prime}}$ find the angle of incidence $\theta_{1}$ in the air that would result in the reflected ray and the refracted ray being perpendicular to each other.

Key Concepts

Reflection

Reflection refers to the process in which light bounces off a surface rather than being absorbed or transmitted. A key principle governing reflection is that the angle of incidence is equal to the angle of reflection, meaning that when light hits a surface at a certain angle, it leaves the surface at the same angle, measured relative to the normal (a line perpendicular to the surface).

Refraction

Refraction is the bending of light as it passes from one medium into another with a different refractive index. This bending occurs because light travels at different speeds in different media, and its change in velocity at the boundary causes the light ray to change direction. The degree of bending depends on the ratio of the refractive indices of the two media.

Snell's Law

Snell’s Law provides the quantitative relationship between the angles of incidence and refraction for a light ray crossing the boundary between two media with different refractive indices. It is stated as n? sin?? = n? sin??, where n? and n? are the refractive indices of the first and second media, and ?? and ?? are the angles of incidence and refraction, respectively. This law is fundamental in determining the path of light as it enters a new medium.

Law of Reflection

The Law of Reflection states that for a reflective surface, the angle at which light is incident upon the surface is equal to the angle at which it is reflected. This principle is essential in analyzing systems where both reflection and refraction occur, as it provides one of the necessary conditions for finding the relationship between the incident, reflected, and refracted rays.

Brewster's Angle

Brewster’s Angle is a specific incidence angle at which the reflected and refracted rays are perpendicular to each other. At this angle, the reflected light is perfectly polarized parallel to the surface. The condition for Brewster’s angle can be derived using the law of reflection and Snell’s Law and results in the relationship tan?? = n?/n?, where n? and n? are the refractive indices of the two media. This concept is crucial when analyzing systems where reflected and refracted rays are constrained to be at 90° to one another.

Transcript

00:02 So this problem involves reflection and reflection.

00:11 And we're actually trying to find an angle of incidence so that the reflected ray and the refracted ray will be perpendicular to each other.

00:20 That angle actually has a name.

00:21 It's called brewster's angle.

00:22 It comes up when you study how polarization happens when a light beam reflects off of a flat surface.

00:32 Let's go ahead and use what we know about the laws of reflection and the law of refraction, or snell's law, this is called.

00:41 First of all, let's look at the reflected ray.

00:44 The reflected ray is going to have an angle of reflection that is equal to the angle of incidence.

00:51 That's just according to the law of reflection.

00:54 So this one over here, this angle over here is also going to be theta 1 if the angle of incidence was theta 1.

01:00 Now down here we have the angle of refraction and we have a law that deals with the angle of refraction.

01:11 It says that if the incident mediums index refraction, that's called it n1 times the sine of theta 1, according to snow's law then, that's going to be equal to the refracting mediums index refraction, and they called it n g here, it's refracting into glass, times the refracting.

01:34 The sign of the angle of refraction.

01:41 But now the angle of refraction and this angle of reflection here, which is equal to the angle of incidence, they have some relationship there because they're supposed to perpendicular.

01:50 And that's the case...

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