# My question is about ray optics particularly image defects

I was learning about spherical abberation and in my book

it is written that when parallel rays pass through lens marginal rays (which are far from principal axis) are bent more than paraxial rays(closer to principal axis)

(considering only thin spherical
lenses)

i am not able to find any explanation of this, and i feel that paraxial rays should bent more which is wrong according the observation

can anyone please provide a intuitive explanation to this... Thankyou

• please edit the question if you think it will make it more helpful Aug 18, 2020 at 12:30
• My answer to Is there a more accurate form of the mirror equation talks about spherical abberation for lenses. Aug 18, 2020 at 13:33

When a ray crosses a boundary between materials with different refractive index, at an angle, it bends.

Here is the ray going straight without bending.

But if it's at an angle, then it does bend.

At a bigger angle it bends more.

If it's a spherical lens, then one or both surfaces fits the shape of part of a sphere.

So the farther you get from the center, the bigger the angle the light ray meets..

So those rays bend more.

• can you please make a drawing or figure to make it more understandabel Aug 18, 2020 at 13:31

Here are two ray diagrams which show the refraction of light by a plano-convex lens.

The right hand diagram is for an ideal lens where all incident rays parallel to the principal axis after refraction pass through the focal point, $$F$$, on the principal axis.

The left hand diagram is for a lens with the right-hand surface being part of a sphere.
Rays close to the principal axis meet in a small region which is the focal "point" but the incident parallel rays a refracted "too much" and miss the focal "point".

The effect is similar when one considers a bi-convex lens and spherical mirrors.