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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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Angular Dispersion and Dispersive Power

Dispersion of light

The phenomena of white light splitting up into different colors when passed through the prism is called dispersion of light. Dispersion happens because refractive index of prism is different for different wavelengths. The white light that strikes the prism surface has multiple colors with different wavelengths. As each wavelength has different refractive index, each color deviates differently trained generates group of colors. This phenomenon of splitting up of white light into multiple colors when it is passing through a material like prism is called as dispersion.

The deviation of the light ray from the original path depends on the refractive index of the material for a given color. We know that among all the colors readies having a highest wavelength and hence lowest refractive index. As a result among all the colors red deviates least and the violet deviates most.

The deviation and refractive index of a local is considered as mean value because it is approximately the average of all the visible colors.

Angular dispersion

The difference in the angle of deviation of any pair of colors is called angle disposition for these two colors.

Angle of deviation is highest for violet color and the lowest for red color. The general angular dispersion that is taken into consideration is the difference between angle of deviation of violet color and the red color.

Angular dispersion depends on the nature of the material of the prism and the angle of the prism.

Dispersive power

The ability of a prism material to disperse the light rays is measured with dispersive power.

It is defined as the ratio of angular disposition between red and violet colors to the main deviation of the colors. As the yellow color deviation is close to the average value, it is treated as the average deviation value and the average refractive index value.

Dispersive power is independent of angle of incidence but depends on the nature of the material.

Dispersion is the phenomena of splitting up of white light into multiple colors. Deviation is the phenomena of taking a different path from the original path after passing through the prism. It is very clear from the discussion that when the light ray passes through a prism it experience both the dispersion as well as the deviation.

Because of the dispersion we are able to see multiple images of a single object which takes the clarity away. Because of the deviation also the original of the image is lost. Though we cannot contain both of them, at least we can eliminate one of them.

We can calculate the total deviation as well as the total desperation generated by the combination of two different prisms as shown below.

Deviation without dispersion

We can use the combination of two different prisms so that they together can produce only deviation and there will not be any dispersion. There is no splitting up of the white color into multiple colors. The phenomena of the white light splitting into multiple colours and creating aberration in the image are called chromatic aberration. With this combination we can eliminate the chromatic aberration and hence the combination is called achromatic combination.

The condition for the deviation without for the dispersion using to prisms is derived as shown below.

Dispersion without deviation

We can arrange the combination of the two prisms in such a way that they will produce only dispersion but not any deviation. This way of arrangement is also called direct vision prism. It can be notice that the emergent light ray from the combination of the two prisms is parallel to the incident light Ray. And hence there is no deviation and there is only dispersion existing. We can derive the equation further as shown below.