# Critical angle/ last angle of refraction

• davidelete
In summary, the glass has an index of refraction of 1.45 and the critical angle is 43.6 degrees. At this angle the light will bounce off all the faces of the pentagon and exit normally.
davidelete

## Homework Statement

A piece of glass has the shape shown in the below diagram. The index of refraction of the glass is 1.45. Find the critical angle for the glass. Sketch the path of the light ray until it emerges from the side of the figure and find the last angle of refraction.

http://img179.imageshack.us/img179/6531/physicsimageez8.png
Sorry if the image is a little ugly...

## Homework Equations

Snell's law

$$n_1\sin\theta_1 = n_2\sin\theta_2\ .$$

## The Attempt at a Solution

sin-1($$\frac{1}{1.45}$$)=43.6 degrees.

I have no idea on how to draw in the diagram. Could someone help me on drawing it? Mine just looks like a bunch of rays bouncing around inside an irregular pentagon on my paper when I try it.

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Are we told the angle at which the light is incident on the glass? Is it incident normally (at 90 degrees)?

astrorob said:
Are we told the angle at which the light is incident on the glass? Is it incident normally (at 90 degrees)?

That is truly everything. I would just have to assume 90 degrees based on the information given.

I don't understand how you're expected to solve that without the incident angle and also the angle at which the glass is sloped on the left hand side.

I suppose it is more of a best guess type of thing. What would your best guess be when drawing a light beam coming in? Where would it bounce to? Where would it exit?

If you don't know what angle its entering the medium relative to the normal then how are you supposed to know if it will internally reflect? It could either exit the medium on the second face or bounce around inside for a while...

As a best guess, and this seems so entirely unphysical that it should have a disclaimer, i'd assume it enters the medium normally, and assume that the angle of the slope is 45 degrees. Since this is a larger angle than critical, it's going to bounce off the lower face, then off the top face, then off the right face, then off the bottom face, and then exit normally out the face it came in through.

astrorob said:
If you don't know what angle its entering the medium relative to the normal then how are you supposed to know if it will internally reflect? It could either exit the medium on the second face or bounce around inside for a while...

As a best guess, and this seems so entirely unphysical that it should have a disclaimer, i'd assume it enters the medium normally, and assume that the angle of the slope is 45 degrees. Since this is a larger angle than critical, it's going to bounce off the lower face, then off the top face, then off the right face, then off the bottom face, and then exit normally out the face it came in through.

Thank you. That was exactly what my best guess looked like as well. Some of the questions on these homeworks are outrageous. I wish they gave more information.

## 1. What is the critical angle of refraction?

The critical angle of refraction is the angle at which a ray of light passing from one medium to another is refracted at an angle of 90 degrees. This means that at the critical angle, the ray will travel along the surface of the second medium instead of passing through it.

## 2. How is the critical angle of refraction calculated?

The critical angle of refraction is calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. The critical angle can be found by setting the angle of refraction to 90 degrees and solving for the angle of incidence.

## 3. What factors affect the critical angle of refraction?

The critical angle of refraction is primarily affected by the refractive indices of the two media. It also depends on the wavelength of light, with shorter wavelengths having a smaller critical angle. Additionally, the surface roughness of the interface between the two media can affect the critical angle.

## 4. What is total internal reflection?

Total internal reflection occurs when a ray of light passing from a medium with a higher refractive index to a medium with a lower refractive index is reflected back into the original medium instead of being refracted. This happens when the angle of incidence is greater than the critical angle, and all of the light is reflected back with no transmission.

## 5. In what real-life applications is the critical angle of refraction important?

The critical angle of refraction is important in a variety of real-life applications, including fiber optic communication, where it is used to ensure that light signals remain within the fiber and are not lost through the sides. It is also used in the design of prisms and lenses, as well as in the phenomenon of mirages, where the critical angle creates the illusion of a pool of water in the distance.

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