Question

The optic axis of a thin equiconvex lens is the x-axis. The co-ordinates of a point object its image are (– 40 cm, 1 cm) and (50 cm, – 2cm) respectively. The lens is located at –

• A. x = + 20 cm
• B. x = – 30 cm
• C. x = – 10 cm
• D. x = 0

Answer 1

Answer: (C)

x = – 10 cm

Answer 2

m = $\frac { - 2 \mathrm {~cm} } { 1 \mathrm {~cm} }$ = –2

\ image is real and inverted

| v | = 2 | u |

| u | = x

| v | = 2x

| u | + | v | = 50 – (– 40) = 90

\ x + 2x = 90

\ x = 30 cm

Hence distance of object from lens is 30 cm and of image is 60 cm. Therefore, the lens should be located at x = –10 cm as in figure.