Question

A figure divided into squares each of size 1 mm², is being viewed at a distance of 9 cm through magnifying lens of focal length 10 cm, held close to the eye.

(a) Draw the ray diagram showing the formation of the image.

(b) What is the magnification produced by the lens? How much is the area of each square in the virtual image?

(c) What is the angular magnification of the lens?

Answer 1

(a) The ray diagram is shown in figure. The virtual image A'B' of real object AB is formed on the same side.

∴ Magnification, m = \(-\frac{v}{u} = \frac{-90}{9} = -10\)

i.e. the image will be erect, virtual and three times bigger.

Magnification in area = (-10)² = 100

Area of the image will be

1 mm² x 100 = 100 mm² = 1 cm²

(c) Angular magnification

= \(\frac{\beta}{\alpha} = \frac{I}{O}\)

= 10.