An object is put at a distance 25 cm from the optical centre of a convex lens. If it's real image is formed at a distance 30 cm from the lens to its focal length is about

(1) 10 cm

(2) 14 cm

(3) 12 cm

(4) 20 cm

Step 1: Given that:

Object distance(u) = $-25cm$

The image of the object formed by the convex lens is real.

Image distance(v) = $+30cm$

(Note:

1. The distances taken left to the optical centre of a lens are taken as negative.
2. The object is placed left to the optical centre of a lens, therefore the object distance is taken as negative.​
3. The distances taken right to the optical centre of a lens, are taken as positive.
4. A real image is formed to the right of a convex lens, therefore the image distance is taken as positive.)

Step 2: Calculation of focal length of the convex lens:

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

Where; u = Object distance , v= image distance and f= focal length of the lens

Putting the given values, we get;

$\frac{1}{+30cm}-\frac{1}{-25cm}=\frac{1}{f}$

$\Rightarrow \frac{1}{30}+\frac{1}{25}=\frac{1}{f}$

$\Rightarrow \frac{1}{f}=\frac{5+6}{150}$

$\Rightarrow \frac{1}{f}=\frac{11}{150}$

$\Rightarrow f=\frac{150}{11}$

$\Rightarrow f=13.6cm$

$\Rightarrow f\approx 14cm$

Thus,

Approximately the focal length of the convex lens is 14cm.