Chromatic Aberration

We are surrounded by all sorts of colors around us

But not always do we manage to capture all the colours perfectly to form a sharp Image

Now this distortion in the image formed can be due to the different coloured lights having different wavelengths

Due to this difference in the wavelength of the different coloured lights, the image formed can be blurry

This is due to the fact that the lights do not converge to a single point

Sometimes the distortion in the final image formed can also be due to a defect in the optical instrument used, i.e. the lens used

The distortion that happens due to the difference in wavelengths of light is called Chromatic Aberration

In Chromatic Aberration, the image formed by the lens is coloured or blurred

As the different coloured lights having different wavelengths fail to converge at a single point, the final images appear blurry

We know that the dispersive power is defined as the ratio of Angular Dispersion and Mean Deviation

Let the focal lengths for red and violet colour be and respectively

Here, is called Longitudinal Chromatic Aberration ( L.C.A.)

Let us now understand Chromatic Aberration in details

L.C.A. is given as, df =

We are well familiar with lens maker’s formula ..(1)

..(1)=Refractive Index of the Medium=Radii of curvature of the first side of the lens=Radii of curvature of the second side of the lens

Differentiate both sides keeping f and as variables, …(2)

From (1) and (2) we can say, So,

This is the aberration. For any lens, it is not possible to have f = 0 or w = 0

Let us see how we can minimise Aberration

Now to reduce chromatic aberration, we are required to focus all the colours to a single point to form a bright sharp image

We know that for a single lens we cannot eliminate aberration. However the overall effect, can be minimized by using a combination of lenses

For two lenses having focal lengths and , the overall focal length () is given by,

Differentiating both sides keeping F as constant,

Now, we already know that

Therefore, the condition for Achromatism is,

Lets understand this condition for Achromatism

We know the dispersive powers of lenses are always positive, which means and are always positive

So, and have to be of the opposite sign; which means if one of our lens is concave, then the other must be convex

Now there are scenarios when we want to make the whole arrangement convering

We know that out of the two lenses that we use; one must be concave while the other convex

We can make the overall arrangement converging by making the focal length of the convex lens less

Revision

The distortion that happens due to the difference in wavelengths of light is called Chromatic Aberration

The condition for Achromatism is given by,

The two Lenses that are used for reducing Chromatic Aberration should be of different nature

The End