Question

The focal length of converging lens is 20 cm. An object is placed at 60 cm from the lens. Where
the image will be formed and what kind of image is?​

Answer 1

Answer:

So, the image will be formed 30 cm behind the lens and the nature of the image is real and inverted.

Explanation:

The converging lens is a concave lens

We know,

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

where, v = image distance, u = object distance and f= focal length

so, given, object distance = 60 cm and focal length = 20 cm

for a convex lens,

the focal length and image distance is positive but the object distance is negative so, u in the formula should be replaced with (-u)

The substituted formula,

$\frac{1}{v} - \frac{1}{(-u)} = \frac{1}{f}\\\\\frac{1}{v}+\frac{1}{u} = \frac{1}{f}$

Substituting the values in the given formula,

$\frac{1}{v} +\frac{1}{60} = \frac{1}{20}\\\\\frac{1}{v}=\frac{1}{20}-\frac{1}{60}\\\\\frac{1}{v} =\frac{3-1}{60}\\\\\frac{1}{v} = \frac{2}{60} = \frac{1}{30}\\\\Hence,\\v =30 cm$

So, the image will be formed 30 cm behind the lens and the nature of the image is real and inverted.