Question

If the focal length of a lens for marginal rays and paraxial rays are $12.5cm$ and $13cm$ respectively, the longitudinal spherical aberration is-
(A) $0.25cm$
(B) $0.5cm$
(C) $0.75cm$
(D) $1cm$

Answer 1

Hint The Paraxial rays are the rays which pass through the principal axis or are very close to it, whereas marginal rays are the rays which pass through the ends of the aperture of the lens. The difference between the image formation by the paraxial and the marginal rays causes spherical aberration.

Complete Step by step solution
In a lens prone to spherical aberration, the image formation by the marginal rays and the paraxial rays is at different lengths. The point of convergence of marginal rays is closer than the point of convergence of paraxial rays. The length between these two points is known as longitudinal spherical aberration.

In the question, focal length of marginal rays$ = 12.5cm$
And focal length of paraxial rays $ = 13cm$
Hence the longitudinal spherical aberration is$ = 13 - 12.5 = 0.5cm$.

Therefore, option (B) is correct.

Additional information In spherical lenses the light is deviated and either converges or diverges. In either case an image is formed at the focus of the lens. But this holds true only for small lenses, as the aperture of the lens is increased, many optical errors arise due to refraction and due to the shape of mirrors.
Spherical aberration arises when the aperture of a spherical mirror is large. Here, the image does not converge at focus, instead the marginal rays are focused closer to the lens while the paraxial rays are focused away from the lens. This results in an unclear image of the object. The plane between these two focal planes where spherical aberration is the lowest, is known as the circle of least confusion.

Note The longitudinal spherical aberration is the distance between the focal points for marginal and paraxial rays. All the rays that pass through the lens form an image inside this region only, this produces an unclear image of the object in the given region.