Tuesday, January 27, 2015

Problems on Angular Dispersion and Dispersive Power

Hallo prism

A beam of white light doesn’t experience any dispersion when it is passed through a Hallo prism. There is no refraction of the light as well as no dispersion of the light in this case. The glass slab with which the prism is made is very thin and behaves like a plain glass. Hence the light rays are passing through it without any dispersion. That is why the when the light is passing through a Hallo prism, no spectrum of light is generated.

Problem and solution

Here we are going to solve some simple problems basing on the dispersion of the light in the dispersive power. When the angle of prism of a small angled prism is given and the refractive index for the different colors is given, we can calculate the angular dispersion between the given to colors as shown.

In another problem we have calculate the dispersive power for the given to colors. This is solved just basing on the formula that we had derived previously.

Problem and solution

In this problem in two different prisms who are small angled prisms, one of the angle of the prism is given and we have to calculate the angle of the prism of the second prism. The corresponding refractive indices of these two prisms for a given color were also given. The condition that is given in the problem is that can be dispersion but not any deviation.

We can solve this problem basing on the condition that is derived for situation where there can be dispersion but there is no deviation as shown below.

Problem and solution

In the problem we have a small angled prism which is first in air and then dipped in the water. We need to calculate how does the minimum deviation is going to be affected when there is a change of the medium.

This can be solved basing on the very definition of the angle of deviation.

Problem and solution

The problem is a combination of two prisms where we need to get dispersion without any deviation. By substituting the basic condition for the given situation we can get the angle of the prism as shown below.

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