Question

Define power of a lens. Write its units. Deduce the relation for two thin lenses kept in contact coaxially.

Answer 1

Answer with Explanation:

Power of lens: It is reciprocal of focal length.

$P=\frac{1}{f}$

S.I unit of power of lens is Diopter  ( D).

Consider two thin lens  A and B of focal length $f_1$ and $f_2$ are kept  in contact coaxially.

Let an  object place at distance u from lens A and it forms real image at I at distance $v_1$ from optical centers of lenses  which act as virtual object for second lens B and it forms final image at I' at distance v from optical centers of two lenses.

For first lens A

$\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}$...(1)

$\frac{1}{f_2}=\frac{1}{v}-\frac{1}{v_1}$....(2)

Adding equation (1) and (2)

$\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Where $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

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