Question

An object when placed in front of a convex lens forms a real image of$0.5$ magnification. If the distance of the image from the lens is $24cm$, calculate focal length of the lens.

Answer 1

Step 1: Given data

Image distance from the lens $\left(v\right)=24cm$

Object distance from the lens$\left(u\right)=?$

magnification$\left(m\right)=0.5$

Focal length$\left(f\right)=?$

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Step 2: calculating the distance of the object

magnification$\left(m\right)=\frac{v}{u}$

$$\begin{gathered} \Rightarrow 0.5=\frac{24}{u} \\ \Rightarrow u=\frac{24}{0.5}=48cm \end{gathered}$$

The distance of the object in the lens is taken as negative.

So, $u=-48cm$

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Step 3: calculating the focal length

Using the lens formula,$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$$\begin{gathered} \frac{1}{f}=\frac{1}{24}-\frac{1}{(-48)} \\ \Rightarrow \frac{1}{f}=\frac{1}{24}+\frac{1}{48} \\ \Rightarrow \frac{1}{f}=\frac{2+1}{48}=\frac{3}{48} \end{gathered}$$

Now, $f=\frac{48}{3}=16cm$

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The focal length of the lens is $16cm$.