Deviation produced by a thin lens | Optics | General theory of image formation

Deviation produced by a thin lens

Deviation produced by a thin lens

In this figure I is the image of the object O.
From ΔOPI,

δ = ∝ + β ...(1)

For paraxial rays ∝ and β are very small.
So, ∝ ≈ tan ∝, and β ≈ tan β
From ΔOPL

∝ ≈ tan ∝ = PL / OL

or ∝ = h / (-u) ...(2)

From ΔPIL,

β ≈ tan β = PL / LI

or β = h / v ...(3)

From equations (1), (2) and (3), we get

$https://latex.codecogs.com/svg.image?\delta =-\frac{h}{u}+\frac{h}{v}$

$https://latex.codecogs.com/svg.image?\delta =h\left ( \frac{h}{u}+\frac{h}{v} \right )$ ...(4)

For thin lens, lens formula is

$https://latex.codecogs.com/svg.image?\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ ...(5)

From equations (4) and (5), we get

$https://latex.codecogs.com/svg.image?\delta=\frac{h}{f}$

Since the value of δ does not depend on ∝ and β.
Therefore all the rays incident at P would suffer the same deviation.

To know more about this topic click on the link https://youtu.be/QDgxZIL8A7k

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