# Methods of Reducing Spherical Aberration

## How to Reduce Spherical Aberration

The following 5 methods are usually used to reduce the spherical aberration.

• By Stop Method.
• By using plano-convex lenses.
• By using two convergent lenses separated by a finite distance.
• By using crossed lens.
• By using the combination of suitable concave and convex lens.

### By Stop Method

Since spherical aberration of a lens depends on the aperture of the lens, so it can be reduced by stopping the marginal rays by placing a stop on the object side of lens.

The stop will block the marginal zones of the lens and only the paraxial zones are exposed to light. Thus, only the paraxial zones are effective and hence the image is formed by the paraxial rays.

Therefore, by stop method, we can form a single point image of a point object. In cameras, the marginal rays are cut off and in case of telescope, paraxial rays are cut off by covering the central portion of the objective lens.

This method of reducing the spherical aberration, however, reduces the intensity of light transmitted by the lens.

### By using plano-convex lenses

As discussed in the previous article of spherical aberration, marginal rays suffer a maximum deviation and hence result in spherical aberration.

If the deviation of the rays can be decreased, then the spherical aberration will be reduced. We know that in a prism, the deviation is minimum when the incident and emergent rays make equal angles with its face.

Similarly, deviation in case of a lens will be minimum if the marginal rays enter first surface of the lens and leave the second surface of the lens at equal angles.

Hence, the spherical aberration can be reduced by designing a lens in such a way that the total deviation of the given ray is divided equally between the two refractions.

In case of a plano-convex lens with its plane face towards the distant object as shown in figure below,

the deviation of the ray is only due to the curved surface and therefore the condition of minimum spherical aberration is violated.

Thus, there is a large spherical aberration in this case. Now if the plano-convex lens is placed with its curved face towards the distant object (as shown in figure),

the deviation is divided between the two surfaces and hence the spherical aberration is reduced considerably.

### By using two convergent lenses separated by a finite distance

Consider two convergent lenses L₁ and L₂ placed at a distance d apart (shown in fig. below). Let their focal lengths be f1 and f2 respectively.

Suppose a ray AB parallel to the axis is incident on the lens L1 and goes along BC after refraction, so that the deviation produces by the lens L1 is δ1. The lens L2 will produce the derivation δ2. From ΔBO1F.

Since δ1 is very small, so

tan δ1 = δ1

Similarly,

The spherical aberration will be minimum, if

δ1 = δ1

Δs BO1F and CO2F are similar

Equating eqns. (1) and (2), we get

Thus, the spherical aberration will be minimum if the two convergent lenses are placed at a distance equal to the difference between their focal lengths.

### By using crossed lens

The longitudinal spherical aberration of a thin lens can be minimized if the form of the lens is biconvex or biconcave such that the radius of curvature R1 of the surface facing the object is 1/6th of that of the other face.

i.e R1 = R2/6. This type of lens is called crossed lens.

### By using the combination of suitable concave and convex lens

Since for a concave lens, the longitudinal spherical aberration is negative and that for a convex lens, it is positive. So by combining the suitable concave and convex lens, the spherical aberration can be cancelled.

### 1 thought on “Methods of Reducing Spherical Aberration”

1. Great article!