Question

an object is placed at 60 cm from a concave lens. The image is formed at a distance of 20 cm from the optical center. Find the focal length of the lens? Is the lens coverging or diverging?
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Answer 1

GiVeN :-

○ Object distance, u = -60 cm

○ Image distance, v = -20 cm

To FiNd :-

• The focal length(f) of the lens.

• If the lens is converging or diverging.

AcKnOwLeDgEmEnT :-

LENS FORMULA is as follows :-

$\displaystyle{\tt{\frac{1}{v}-\frac{1}{u}=\frac{1}{f} }}$

SoLuTiOn :-

Applying the lens formula :-

$\displaystyle{\tt{\frac{1}{v}-\frac{1}{u}=\frac{1}{f} }}$

$\displaystyle{\tt{\longrightarrow \frac{1}{-20}-\frac{1}{-60}=\frac{1}{f} }}\\\\\displaystyle{\tt{\longrightarrow \frac{-1}{20}+\frac{1}{60}=\frac{1}{f} }}\\\\\displaystyle{\tt{\longrightarrow \frac{-3+1}{60}=\frac{1}{f} }}\\\\\displaystyle{\tt{\longrightarrow \frac{-2}{60}=\frac{1}{f} }}\\\\\displaystyle{\tt{\longrightarrow \frac{-1}{30}=\frac{1}{f} }}\\\\\boxed{\boxed{\displaystyle{\tt{\longrightarrow f=-30\ cm}}}}$

$\rule{200}3$

A concave lens is called as 'Diverging lens'.

When light passes through the lens, it bends the light rays towards each other.

The concave lens spreads out the light when it passes through the lens.

Answer 2

Given

An object is placed at 60 cm from a concave lens. The image is formed at a distance of 20 cm from the optical center.

To find

Find the focal length of the lens? Is the lens coverging or diverging?

Solution

• Object distance (u) = -60cm
• Image distance (v) = - 20cm
• Focal length (f) = ?

Apply lens formula

$\implies\sf \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f} \\ \\ \\ \implies\sf \dfrac{-1}{20}-\dfrac{-1}{60}=\dfrac{1}{f} \\ \\ \\ \implies\sf \dfrac{-3+1}{60}=\dfrac{1}{f} \\ \\ \\ \implies\sf \dfrac{1}{f}=\dfrac{-2}{60} \\ \\ \\ \implies\sf f=-30cm$

Hence, the focal length of concave lens is -30cm and it is a diverging lens