Power of lens | Units | Combination in series and parallel - Param Himalaya

Power of lens | Units | Combination in series and parallel - Param Himalaya 

Power of a lens

Power of a lens is a measure of the convergence or divergence.

The power $P$ of a lens is defined as the tangent of the angle by which it converges or diverges a beam of light parallel to the principal axis falling at unit distance from the optical centre.

$\tan \delta = \frac{h}{f}$ 

if h = 1 then 

$\tan \delta = \frac{1}{f} \text{ or } \delta = \frac{1}{f}$

$\text{ for small } \delta.$

That is,

$P = \frac{1}{f_{(\text{in m})}} \quad \dots (i)$

or,

$P = \frac{100}{f_{(\text{in cm})}}$

As per lens maker's formula, the focal length of a lens is given by 

$\frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$

$\therefore$ Power of lens,

$P = \frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \quad \dots (ii)$

Thus, power of a lens is more if its focal length is small and power of a lens is less if its focal length is large.

SI unit of power :

The SI unit of power is dioptre and denoted by D.

$P = 1$ dioptre if $f = 1$ metre

Thus, the power of lens is 1 dioptre if its focal length is 1 metre.

$1 \text{ D} = 1 \text{ m}^{-1}$

A lens of short focal length has more power whereas  a lens of long focal length has less power.

The power of a convex lens is positive

The power of a concave lens is negative.

In order to calculate the power of a lens , we need its focal length in metres.

Power of a combination of lenses : 

1.If two lenses are placed in contact , the combination has a power equal to the algebraic sum of the powers of two lenses.

P = P1+ P2 , 1/f = 1/f1 + 1/f2