A thin converging lens with a focal length of 20\text{ cm} is placed in direct contact wit… — JAMB UTME

A thin converging lens with a focal length of $20\text{ cm}$ is placed in direct contact with a thin diverging lens with a focal length of $50\text{ cm}$ . What is the combined optical power of this two-lens system in dioptres?

$+3.0\text{ D}$ Answer
B
$+7.0\text{ D}$
C
$-3.0\text{ D}$
D
$+0.03\text{ D}$

Answer

The combined optical power of the lens system is

+3.0\text{ D}

The individual power of the converging lens is

+5.0\text{ D}

and the power of the diverging lens is

-2.0\text{ D}

. Summing these values algebraically yields a net power of

+3.0\text{ D}

Step-by-Step Solution

Convert the focal length of each lens from centimeters to meters and apply sign conventions.

Converging lens focal length

f_1 = +0.20\text{ m}

; Diverging lens focal length

f_2 = -0.50\text{ m}

Optical power in dioptres requires focal length to be expressed in meters, with converging lenses being positive and diverging lenses being negative.

Calculate the individual power of each lens.

P_1 = \frac{1}{+0.20} = +5.0\text{ D}

and

P_2 = \frac{1}{-0.50} = -2.0\text{ D}

Power of a thin lens is defined as

P = \frac{1}{f}

where

f

is in meters.

Sum the individual powers to find the total power of thin lenses in contact.

P = P_1 + P_2 = +5.0\text{ D} + (-2.0\text{ D}) = +3.0\text{ D}

When thin lenses are in contact, their net optical power is equal to the algebraic sum of their individual powers.

Key Concept

Power of Thin Lenses in Contact

Estimated Time:1m 15s

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