# For which incidence angle the ray won't come out of the prism's surface....

In summary: This means that the rays, irrespective of the incident angle, will undergo total internal reflection at the second surface.

## Homework Statement

A ray of light falls on the surface AC of a prism with a straight angle and with two sides equal. For which incidence angle the ray won't come out of the surface AB. The index of refraction for the prism is n=2.

sina/sinb=n2/n1

## The Attempt at a Solution

sinb=1 so sina=n2/n1=1/2 the angle is pi/6 rad. Am I right?

Give us the related picture.

blue_leaf77 said:
Give us the related picture.
http://s32.postimg.org/6fsfdz69x/image.png
I am adding: pi/6 rad is the angle of incidence. The first refracted angle is pi/3 rad. sin pi/3/sina=1/2
sin a=1.7. Where am I wrong?

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What is the prism apex angle? In the problem statement you said "straight angle", but what does straight mean in this case? Googling this term resulted in a straight angle being equal to 180 degrees.

blue_leaf77 said:
What is the prism apex angle? In the problem statement you said "straight angle", but what does straight mean in this case? Googling this term resulted in a straight angle being equal to 180 degrees.
It is pi/2 rad or 90 degrees.

Take a look at the picture below,

since you know that exit angle at the last surface is 90 degrees, you should be able to calculate ##\delta##, then ##\epsilon##, afterwards ##\gamma## follows naturally from that upper triangle and so on till you find ##\alpha##.

sin sigma/sin 90=1/2=> sin sigma= pi/6 rad. beta=180-90-30=60=pi/3 rad. (as the angle of two extensions is pi/2.
sin alpha/ sin 60=2/1=> sin alpha/sqrt(3)/2=2=> sin aplha=sqrt (3)=1.7. I don't know where I am wrong.

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blue_leaf77 said:
Just did it.

This potentially means that any incident angle on a right angle prism with ##n=2## will result in a total internal reflection at the second surface and hence no light can be transmitted.

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blue_leaf77 said:
This potentially means that any incident angle on a right angle prism will result in a total internal reflection at the second surface and hence no light can be transmitted.
What about the two equal sides of the prism. i didn't use this fact anywhere.

Probably that means the prism is an isosceles triangle but that doesn't influence the propagation of the ray. Anyway you can actually prove the statement I made in post #10. Denote the exit angle out of the second side as ##\eta##. In the second surface, Snell's law gives ##n \sin \delta = \sin \eta##. Then ##\beta = 90^o-\delta## and Snell's law in the first side gives
\begin{aligned} \sin \alpha &= n \sin\beta = n \sin(90^o-\delta) \\ &= n\cos \delta = n \sqrt{1-\sin^2 \delta} \end{aligned}
Then by substituting Snell's law from the second side for ##\sin \delta##,
$$\sin \alpha = n \sqrt{1-\frac{\sin^2 \eta}{n^2}} \\ \sin \alpha = \sqrt{n^2 - \sin^2 \eta}$$
The maximum value for the left side is unity, while the minimum value for the right side with ##n=2## is ##\sqrt{2^2-1} = \sqrt{3}##. This means, for any incident angle ##0\geq \alpha \geq 90^o##, there is no real solution for the exit angle ##\eta##. Physically, this means that the rays, irrespective of the incident angle, will undergo total internal reflection at the second surface.

## 1. What is the principle behind a prism's ability to refract light?

A prism is a transparent optical element with flat, polished surfaces that can refract, reflect, and disperse light. This is due to the fact that the speed of light changes when it travels through different mediums, causing it to bend or refract when it passes through the prism's surfaces at different angles.

## 2. How does the angle of incidence affect the refraction of light in a prism?

The angle of incidence, or the angle at which light enters a prism, is a crucial factor in determining the amount of refraction that occurs. If the angle of incidence is small, the angle of refraction will be larger and the light will bend more as it passes through the prism. On the other hand, if the angle of incidence is large, the angle of refraction will be smaller and the light will bend less.

## 3. What is the critical angle of a prism and how does it relate to the incident angle?

The critical angle of a prism is the angle of incidence at which the refracted ray just grazes along the surface of the prism. This means that any incident angle greater than the critical angle will result in total internal reflection, where the light will not exit the prism's surface. The critical angle is directly related to the refractive index of the prism, which is a measure of how much the speed of light changes when passing through the prism's material.

## 4. Is there an incidence angle at which the ray will not come out of the prism's surface?

Yes, there is an incidence angle at which the ray will not come out of the prism's surface. This angle is known as the critical angle and it depends on the refractive index of the prism's material. If the angle of incidence exceeds the critical angle, the light will be totally reflected back into the prism, resulting in no refraction or transmission of light.

## 5. How can the refractive index of a prism's material be determined?

The refractive index of a material can be determined by measuring the angle of incidence and the angle of refraction as the light passes through the prism. By using Snell's law, which relates the angles of incidence and refraction to the refractive index, the value of the refractive index can be calculated. Additionally, the refractive index can also be found by using a spectrophotometer or through experimental methods such as measuring the critical angle of the prism.

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