Question

A lens of focal length 20 cm forms an inverted image at a distance 60 cm from the lens.

1. Identify the lens.
2. How far is the lens present in front of the object?
3. Calculate the magnification of the image.

Answer 1

(i) The lens is a convex lens.

(ii) Given values according to sign convention:

Focal length (f) = +20 cm (Positive for a convex lens forming a real image

Image distance (v) = +60 cm (Positive because real/inverted images form behind the lens)

Using the Lens Formula:

`1/v - 1/u = 1/f`

`1/60 - 1/u = 1/20`

`-1/u = (3 - 1)/60`

`-1/u = 2/60`

`-1/u = 1/30`

u = −30 cm

The lens is present at a distance of 30 cm in front of the object.

(iii) Using the Magnification Formula for a lens:

m = `v/u`

= `60/-30`

= −2

The magnification of the image is −2 (the minus sign confirms that the image is inverted).