A thin converging lens forms a real image of an object on a screen placed 60\text{ cm} fro… — JAMB UTME

A thin converging lens forms a real image of an object on a screen placed $60\text{ cm}$ from the lens. If the object is located $30\text{ cm}$ in front of the lens, what is the focal length of the lens in centimeters ( $\text{cm}$ )?

Answer: 20 cm

Answer

The focal length of the converging lens is

20\text{ cm}

Using the thin lens formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

with an object distance

u = 30\text{ cm}

and a real image distance

v = 60\text{ cm}

yields

\frac{1}{f} = \frac{1}{30} + \frac{1}{60} = \frac{1}{20}

, giving

f = 20\text{ cm}

Step-by-Step Solution

Identify given parameters and apply correct sign conventions

u = +30\text{ cm}

(real object) and

v = +60\text{ cm}

(real image on screen)

In thin lens calculations for real objects and images formed on screens, both distances are positive.

Substitute parameters into the thin lens formula

\frac{1}{f} = \frac{1}{30} + \frac{1}{60}

The thin lens equation relates focal length

f

, object distance

u

, and image distance

v

Perform fraction addition and solve for focal length

\frac{1}{f} = \frac{3}{60} = \frac{1}{20} \implies f = 20\text{ cm}

Taking the common denominator gives

\frac{1}{20}\text{ cm}^{-1}

, which yields

f = 20\text{ cm}

Key Concept

Thin Lens Formula for Real Image Formation

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