An object is placed at 30 cm in front of the convex lens of focal length 10 cm. Find out the image distance from lens?

Step 1: Given that:

Object distance($u$) = $-30cm$

Focal length($f$) of convex lens= $+10cm$

(Note;

1. The object distance is taken as negative as it lies in the left to the optical centre of the lens.
2. The focal length of the convex lens is positive as the focus of the convex lens lies in the right of optical centre.)

Step 2: Calculation of image distance:

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

Where u = Object distance

v= Image distance

f = Focal length of the lens

Putting all the values we get;

$\frac{1}{v}-\frac{1}{-30cm}=\frac{1}{+10cm}$

$\frac{1}{v}+\frac{1}{30}=\frac{1}{10}$

$\frac{1}{v}=\frac{1}{10}-\frac{1}{30}$

$\frac{1}{v}=\frac{3-1}{30}$

$\frac{1}{v}=\frac{2}{30}$

$v=+15cm$

Thus,

Option c) $+15cm$ is the correct option.