Aberration of Lens

Science is an interesting subject that is based on application through experimentation and observation. Students are required to read and learn the Concepts of science to understand the basic things happening in and around our surroundings. There are mainly three divisions of science namely, Physics, Chemistry and Biology.

Physics is considered to be a stream of Science that studies matter and its entities of energy and force. Physics is an important part of science that reasons and solves  the basic and most important aspects of real life like Electricity, car seat belts, electrical appliances and much more. In this article, students will find all the necessary details about Aberration of lens.

Suppose I have a lens and an object in front of it. Generally, we see the object with white light (having a spectrum of colours), so we call it a white light object. 

When I see this object through the lens, the rays of different focal lengths form different images, and we get a blurred image of the object. 

Ideally, these rays should focus at a point on the lens and form a single image, but we get different images at different points. This image error is caused because of the defect called the ‘Aberration of a lens’.

In this article, we will study the types of aberration in lenses and the ways to reduce them.

Types of Aberration of Lenses

The types of aberrations are:

1. Spherical Aberration

2. Chromatic Aberration

3. Astigmatism

4. Distortion

5. Field Curvature

6. Coma

7. Zernike Polynomials

1. Spherical Aberration

An optical defect in a lens is called the spherical aberration because we cannot see the objects with clarity. The two causes of spherical aberration are:

• Low-quality Lens

• Large aperture Lens

In this type of aberration, the light rays passing through the lens don’t converge at the common point. There are two causes of spherical aberration in lenses. Let’s discuss these one-by-one:

The rays coming from the margin (or far away) are called the marginal lines. These lines meet at a point close to the centre of the axis at a focal length fm. 

The rays nearer to the centre are called paraxial rays. These paraxial rays of different focal lengths form images at different focal points on the axis. 

Because of the formation of multiple images of the same object, we get a low-resolution/blur image on the lens.

2. Chromatic Aberration                         

We know that white light is composed of seven colours and each colour has its focal length & wavelength. When this light passes through the lens, the colours of different focal lengths form images at different spots on the axis. Because of this, we get a blurred image of the object. This type of defect is called chromatic aberration.

There are two types of chromatic aberrations, these are:

Longitudinal

• Lateral Chromatic Aberration

• Longitudinal Aberration

Longitudinal chromatic aberration is also called the axial chromatic aberration. A lens cannot focus rays of light with different focal lengths on the same focal plane. 

Lateral Aberration

This aberration is also called the transverse chromatic aberration. 

Lateral aberration is a type of aberration that causes colour fringing as a result of image magnification which varies with colour wavelength. 

A secondary chromatic aberration is also related to lateral chromatic aberration. This secondary chromatic aberration causes difficulty in the simultaneous correction of blue, green, and red light rays.

3. Astigmatism

This aberration is similar to chromatic aberration because, in both, the object lies off the principal axis. This type of aberration causes a sharp image to appear as an ellipse away from the focal plane, with the long axis of the ellipse shifting by 90° on the opposite sides of the focal plane.

Combination of 2 Lenses to Reduce Chromatic Aberration

Let’s consider a white light after passing through the lens dispersed into three colours, i.e., violet, red, and yellow.

We know that the focal length of red is greater than the violet colour, i.e. Fr > Fv, so chromatic aberration = Fr - Fv

The condition for a minimum chromatic aberration is: Fr - Fv should be equal to zero. This is what we are going to prove further.

Here, we will use the lens maker’s formula for red and violet light forming images at different points on the lens:

 \[\frac {1}{Fr} = (\mu_{r} - 1) (\frac {1}{R1} - \frac {1}{R2})\] ..(a)  

\[\frac {1}{Fv} = (\mu_{v} - 1) (\frac {1}{R1} - \frac {1}{R2})\] …(b)

F_r - F_v =  F_r F_v\[(\mu_{v} - \mu_{r}) (\frac {1}{R1} - \frac {1}{R2})\]...(c)

For yellow light, the formula is:

\[\frac {1}{Fy} = (\mu_{y} - 1 ) (\frac {1}{R1} - \frac {1}{R2})\] ....(d)

\[\frac {Fr - Fv}{FrFv} = (\mu_{v} - \mu_{r} ) (\frac {1}{R1} - \frac {1}{R2}) * \frac {(\mu{y} -1)} {(\mu{y} -1)} = \frac {(\mu{v} - \mu{r})} {(\mu{y} -1)} * (\mu{y} -1) * (\frac {1}{R1} - \frac {1}{R2}) \]

From equation (d), we have:

\[\frac {Fr - Fv}{FrFv} = \frac {(\mu{v} - \mu{r} )} {(\mu{y} -1)} * \frac {1}{Fy} \] …..(e)

We know that prism is a special type of lens whose dispersive power, ω = \[\frac {(\mu {v} - \mu{r})} {({\mu{y} -1})}\]

So, from equation (e), we get,

 \[\frac {Fr - Fv}{FrFv} = \omega * \frac {1}{Fy} \]

Now, if we do F_r * F_v,  we can see that the geometric progression for F_y, i.e. F_r * F_v = Fy²

So, \[\frac {Fr - Fv}{Fy^2} = \omega * \frac {1}{Fy} \Rightarrow F_r -F_v = \omega * F_y \]

We also know that more is the dispersive power (ω), more will be an aberration.

On putting the value of ω as zero, we get  F_r - F_v = zero. 

Now, we can see that there is no difference between the focal lengths of light and the rays that meet at the common point.

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