What is the smallest angle θ1 for which a laser beam will undergo total internal reflection on t

step 1 In this question, we have this right angle glass prism. We want to find a smallest angle, theta

What is the smallest angle θ1 for which a laser beam will...

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Key Concepts

Total Internal Reflection

This is an optical phenomenon that occurs when a light ray traveling within a medium of higher refractive index strikes the boundary with a medium of lower refractive index at an angle greater than a certain critical angle, leading to the light being completely reflected back into the original medium rather than refracted out.

Critical Angle

The critical angle is the minimum angle of incidence inside a medium at which total internal reflection occurs. It is determined by the refractive indices of the two media and provides the boundary condition between refraction and total internal reflection.

Snell's Law

Snell's Law is a fundamental equation in optics that relates the angles of incidence and refraction to the refractive indices of the two media. It is essential for calculating the path of light as it transitions between media and plays a key role in determining the conditions for total internal reflection.

Refractive Index

The refractive index is a measure of how much the speed of light is reduced inside a medium compared to its speed in a vacuum. It is a critical parameter in determining the bending of light at interfaces and is used in calculations involving Snell's Law and the critical angle.

Transcript

00:01 In this question, we have this right angle glass prism.

00:05 We want to find a smallest angle, theta 1, such that the laser beam will undergo a total internal reflection on the hypotenance of the prism.

00:19 So this problem is about refraction and total internal reflection.

00:27 So we first need to draw a few rays.

00:34 So as the incoming ray hits this surface, it would get bent toward the normal, like this, and then you draw normal here, and then you want it to undergo total internal reflection.

00:55 So the light ray would emerge like this.

00:58 And so this is our data c.

01:04 So why is it? okay, so theta one is the smallest.

01:08 So that means our data 2 will also be the smallest.

01:13 Okay, so we extend this horizontal line to here.

01:17 Okay, we want to find out how what's the angle data c is like.

01:23 So this is 60 degrees.

01:26 This angle here is 120 degrees.

01:30 And then we also want to find out this is angle.

01:33 Okay, so this angle here is 60 degrees minus data 2.

01:43 Okay, and from the diagram, we have 60 degrees minus data 2 plus data c is equal to 90 degrees.

01:54 Okay, so if data 1 is the smallest, that means data 2 is the smallest...