(II) A triangular prism made of crown glass (n=1.52) with...

(II) A triangular prism made of crown glass $(n=1.52)$ with base angles of $30.0^{\circ}$ is surrounded by air. If parallel rays are incident normally on its base as shown in Fig. $53,$ what is the angle $\phi$ between the two emerging rays?

Key Concepts

Prism Geometry

Understanding the geometry of a prism, including the angles of its faces and its overall shape, is vital in solving problems involving light deviation. The angular relationships and dimensions of the prism directly influence the path of the light within it and the resulting direction of the emerging rays.

Angular Deviation

Angular deviation refers to the overall change in direction of a light ray as it passes through an optical element like a prism. This concept encompasses the initial bending upon entering the medium, further changes within the medium due to its geometry, and the subsequent bending upon exit.

Snell's Law

This fundamental law of refraction relates the angles and refractive indices of two different media. It describes how a ray of light bends when entering a medium with a different optical density, using the relationship n? sin(??) = n? sin(??). This concept is essential for calculating the change in direction of light as it passes from one medium to another.

Refractive Index

The refractive index of a medium quantifies how much it reduces the speed of light compared to vacuum. It is a crucial parameter in optics because it determines the degree to which light is bent, or refracted, when it enters or exits that medium.

Transcript

00:01 Okay.

00:03 In this problem, we have a prism shown to the right that has angles 30 degrees, and we have instant light that passes through the prism, and upon leaving the prism, get refracted, and cross with some angle fee.

00:15 If the prism has an index or refraction, which we're going to call n of 1 .52, we want to find what fee is.

00:22 So this is essentially an application of snell's law for refraction with some relevant trigonometry.

00:29 So we recall, snell's law simply states that the product of index refraction and the sign of angle is the same on both sides of a boundary with two different indices of refraction.

00:42 So it's expressed mathematically, n1 sine theta 1 equals n2 sine theta 2, where the angles are incident and refracted angle, respectively, for the light.

00:52 So to start us off, we can apply this to the rays as they exit the prism and get refracted because we know the index of refraction for air is 1.

01:02 And we know it for the material it's exiting, which will allow us to solve for everything we need.

01:10 Now, starting off with snow's law, n1, sine theta 1, equals n2 sine theta 2.

01:19 We got to apply these properly.

01:25 We can solve for the refracted angle, theta r.

01:29 Well, let's call it theta 2 just to be consistent.

01:33 It's equal to inverse sign of the ratio 1 .52 over 1, sine, sine, and theta 1...

Please give Ace some feedback