A converging lens has a focal length of 25\text{ cm}. What is the optical power of the len… — JAMB UTME

A converging lens has a focal length of $25\text{ cm}$ . What is the optical power of the lens in dioptres?

The optical power of the lens is

+4.0\text{ D}

The optical power

P

of a lens in dioptres (

\text{D}

) is calculated using

P = \frac{1}{f}

, where

f

is the focal length in metres. Converting

25\text{ cm}

to metres gives

0.25\text{ m}

. Since the lens is converging, its focal length is positive (

+0.25\text{ m}

). Thus,

P = \frac{1}{+0.25} = +4.0\text{ D}

Convert the focal length from centimetres to metres

f = 25\text{ cm} = 0.25\text{ m}

The unit of optical power (dioptre,

\text{D}

) requires the focal length to be expressed in metres.

Apply the sign convention for a converging lens

f = +0.25\text{ m}

A converging (convex) lens has a real principal focus, so its focal length is positive by sign convention.

Calculate the optical power using the formula

P = \frac{1}{f}

P = \frac{1}{+0.25} = +4.0\text{ D}

Optical power is defined as the inverse of the focal length in metres.

Power of a Thin Lens

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