Question

How far should an object be placed at from a convex lens of focal length 20cm to obtain its real image at a distance of 30 cm from the lens determine the height of the image if the object is 4cm tall

Answer 1

Given :-

Focal length (f) = 20cm

Image distance (v) = 30cm

Height of object (h) = 4cm

Nature of image = Real, Inverted.

Object distance (u) = ?

Height of image (h') = ?

Solution :-

(i) Lens formula :- 1/v - 1/u = 1/f

So,

1/u = 1/v - 1/f

Substituting values,

1/u = 1/30 - 1/20

1/u = 20 + 30/600

1/u = 50/600

1/u = 5/60

1/u = 1/12

u = +12cm

•°• Object distance is 12cm.

(ii) Magnification (m) = h'/h = v/u

or,

h' = h(v)/u

Substituting values,

h' = (4 x 30)/12

h' = 120/12

h' = 10

•°• Height of image is 10cm.