Question

(i) Define the term power of a lens. Write its SI units.

(ii) Derive the expression for the power of two thin lenses placed in contact with each other.

Answer 1

(i) Power of lens is the reciprocal of its focal length in metre.

i.e. P = \(\frac{1}{\text {f (in m)}}\)

SI units of power is dioptre (D).

(ii) Power of two thin lenses in contact

Derivation of the relation

\(\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}\)

Consider an object O placed at a distance u on principal axis of the lens A. Rays of light starting from O form the image I₁.

∴ \(\frac{1}{v_1} - \frac{1}{u} + \frac{1}{f_1}\) ...........(1)

Place the lens B in contact with A. The image I₁, will serve as virtual object and forms a real image I.

The total power of the lens combination is given by

P = P₁ + P₂

If the two lens of focal lengths f₁ and f₂ are placed at a distance x apart, then the focal length of the combination will be:

The power of combination is given by

P = P₁ + P₂ - xP₁P₂