Question

A convex lens produces an image of an object on a screen with a magnification of $\frac{1}{2}$ .When the lens is moved 30 cm away from the object, the magnification of the image is 2.The focal length of the lens is

• A. 20 cm
• B. 25 cm
• C. 30 cm
• D. 35 cm

Answer 1

The correct option is A 20 cm

We know that

$m=\frac{f-v}{f}$

As given,

$\frac{1}{2}=\frac{f-v}{f}f=2(f-v)f=2f-2v2v=2f-f2v=fv=\left(\frac{f}{2}\right)\to \left(i\right)$

Now we have$m=2$

and $v^1=(v+30)$

$\Rightarrow m=\frac{f-v}{f}Rightarrow2=\frac{f-(v+30)}{f}\Rightarrow 2=\frac{f-(f/2+30)}{f}\left(from\right(i\left)\right)$

$2f=f-f/2+30\Rightarrow 2f=\frac{f}{2}+30\Rightarrow 2f-\frac{f}{2}=30cm\Rightarrow \frac{4f-f}{2}=30cm\Rightarrow \frac{3f}{2}=30\Rightarrow 3f=60\Rightarrow f=20cm$