# Reflecting Prism Homework: Min Refractive Index & Ray Path

• crystalplane
In summary, a reflecting prism is an optical prism that reflects and redirects light using two triangular prisms joined at their base. The minimum refractive index for a reflecting prism is 1.414, which is determined by the angle of incidence and angle of reflection using Snell's law. The path of light inside a reflecting prism is dependent on these factors, with the critical angle being the point at which light passes through the prism instead of being reflected. The critical angle can be calculated using the inverse sine of the prism's refractive index.
crystalplane

## Homework Statement

a)What is the minimum refractive index of the prism in order for the light to reflect?
b) What is wrong with this ray path for a reflecting prism?

## Homework Equations

nisin(theta 1)= ntsin(theta 2)

## The Attempt at a Solution

for part a, nt is 1, theta 2 is 90 degree, theta 1 is 50 degree,
then i got ni = 1.3
For part b, i have no idea about it..

#### Attachments

• 12.jpg
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the graph is attached now...

The minimum refractive index for a reflecting prism to work is 1.5, as anything less than that would result in total internal reflection. Total internal reflection occurs when the angle of incidence is greater than the critical angle, causing all the light to be reflected back into the medium instead of passing through the prism.

As for the ray path, the issue lies in the angles of incidence and refraction. In order for a reflecting prism to work properly, the angle of incidence should be equal to the angle of reflection. However, in this ray path, the angle of incidence (50 degrees) is not equal to the angle of reflection (90 degrees). This would result in a distorted image being produced by the prism. The correct ray path should show the light entering the prism at an angle of 45 degrees, reflecting off the hypotenuse at 45 degrees, and exiting the prism at an angle of 45 degrees. This ensures that the angle of incidence is equal to the angle of reflection, resulting in a clear and undistorted image.

## 1. What is a reflecting prism?

A reflecting prism is a type of optical prism that is used to reflect and redirect light. It consists of two triangular prisms joined together at their base, with one of the prisms coated with a reflective material such as aluminum or silver. When light enters the prism, it is reflected off the coated surface and exits the prism at a different angle.

## 2. What is the minimum refractive index for a reflecting prism?

The minimum refractive index for a reflecting prism is 1.414, which is the refractive index of the material used to coat the prism's surface. This ensures that light is fully reflected off the surface and does not pass through the prism, resulting in a clear and distinct image.

## 3. How is the minimum refractive index determined for a reflecting prism?

The minimum refractive index for a reflecting prism is determined by the angle of incidence and angle of reflection. The minimum refractive index is calculated by dividing the sine of the angle of reflection by the sine of the angle of incidence. This is known as Snell's law.

## 4. What is the path of light inside a reflecting prism?

The path of light inside a reflecting prism depends on the angle of incidence and the refractive index of the prism. When the angle of incidence is greater than the critical angle, the light is reflected off the coated surface and exits the prism at a different angle. However, if the angle of incidence is less than the critical angle, the light will pass through the prism and be refracted.

## 5. What is the critical angle for a reflecting prism?

The critical angle for a reflecting prism is the angle of incidence at which the light is no longer reflected off the coated surface and instead passes through the prism. It can be calculated by taking the inverse sine of the refractive index of the prism.

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