The prism shown in Fig. P33.49 has a refractive index of...

The prism shown in Fig. P33.49 has a refractive index of 1.56 , and the angles $A$ are $27.0^{\circ}$. Two light rays $m$ and $n$ are parallel as they enter the prism. What is the angle between them after they emerge?

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another with a different refractive index. This change in direction occurs because light travels at different speeds in different materials, and it is governed by the principles of optics.

Snell's Law

Snell's law quantitatively describes how light is refracted at an interface between two media. It relates the sines of the angles of incidence and refraction to the refractive indices of the two materials, allowing one to calculate the bending of light as it enters or exits a prism.

Prism Deviation

Prism deviation refers to the overall change in direction of a light ray after it passes through a prism. This deviation is determined by the geometry of the prism, the angles at each face, and the refractive index of the prism material, and it is calculated by applying Snell's law at each interface.

Transcript

0:00 Hi.

00:01 Here in this given problem there is an isoseless prism having two equal angles which are represented as a each.

00:24 These are 27 degrees.

00:27 The two rays entering into the prism perpendicular to the base, the rays will enter undivated for the perpendicular.

00:42 For the normal incidence, refraction will fail like this.

00:48 So now if we look for the angle of incidence made by these rays to the opposite face with the opposite face, withdraw the normals like this.

01:04 So these angles using geometry, each angle of incidence comes out to be equal to 27 degree angle of incidence.

01:17 Identical for both the rays.

01:20 Okay.

01:22 Now as these rays are going out in the air from the glass, so they will deviate away from the normal.

01:31 Means the rays will go like this.

01:38 And now the rays will intersect at some point and we have to find the angle at which they will meet with each other after coming out of the prism for which we will find this angle.

01:59 To find this angle we should find this one, means this one which is angle of refraction.

02:11 After finding it we will subtract it from 90 degree which will give us this angle and this complete angle also will be found then it will be divided into two parts then here it will be 180 minus this angle and ultimately we can find this angle.

02:29 So first of all, the rays are m and n.

02:35 So for each ray using snell's law, while the ray will be going out of the glass into the air, sine i by sine r, that is 1 by 1 .56, the refractive index of the glass...

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