# Aberration of Lens

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

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

2. The rays nearer to the center 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 colors and each color has its focal length & wavelength. When this light passes through the lens, the colors 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:

1. Longitudinal

2. 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 color fringing as a result of image magnification which varies with color 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 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 disperse into three colors, i.e., violet, red, and yellow.

We know that the focal length of red is greater than the violet color, 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:

$\frac{1}{Fr}$= (μr - 1)($\frac{1}{R1}$ - $\frac{1}{R2}$) ..(a)

$\frac{1}{Fv}$ = (μv - 1)($\frac{1}{R1}$ - $\frac{1}{R2}$)…(b)

Fr - Fv =  Fr Fvv - μr)($\frac{1}{R1}$ - $\frac{1}{R2}$)...(c)

For yellow light, the formula is:

$\frac{1}{Fy}$ = (μy - 1)($\frac{1}{R1}$ - $\frac{1}{R2}$) ....(d)

$\frac{Fr - Fv}{FrFv}$ = (μv - μr)($\frac{1}{R1}$ - $\frac{1}{R2}$) * $\frac{(μy-1)}{(μy-1)}$ = $\frac{(μv-μr)}{(μy-1)}$ * (μy - 1) * ($\frac{1}{R1}$ - $\frac{1}{R2}$)

From equation (d), we have:

$\frac{Fr - Fv}{FrFv}$ =  $\frac{(μv-μr)}{(μy-1)}$ *  $\frac{1}{Fy}$ …..(e)

We know that prism is a special type of lens whose dispersive power, ω = $\frac{(μv-μr)}{(μy-1)}$

So, from equation (e), we get,

$\frac{Fr - Fv}{FrFv}$  =  ω* $\frac{1}{Fy}$

Now, if we do Fr * Fv,  we can see that the geometric progression for Fy, i.e. Fr * Fv = Fy2

So, $\frac{Fr - Fv}{Fy^{2}}$  =  ω* $\frac{1}{Fy}$ ⇒ Fr - Fv = ω* Fy

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  Fr - Fv = zero.

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

Question 1: What is an Aberration in photography?

Answer: The aberration that occurs in photography is the chromatic aberration. This defect occurs because of the two following reasons:

1. The lens is unable to bring lights of different wavelengths to the same focal plane, or

2. Lights of different focal lengths form different images at different focal points.

Question 2:  What is Coma?

Answer: Coma is a type of aberration that occurs due to the refraction differences when light rays pass through the different zones of the lens.

This aberration is integral to certain optical designs or the imperfection in the lens or other components resulting in off-axis point sources. Due to this defect, people view the distorted image of the objects.

Question 3: What is the Distortion?

Answer: Distortion is a type of aberration. This aberration occurs when there are variations in the focal lengths of the lens with distance away from the principal axis. The straight object seems to be distorted. The common examples of this type of aberrations are:

1. Barrel

2. Pincushion

Question 4: Write about the Positive and the Negative Lens.