Question

A convex lens has focal length 20 cm, which produces an image four times larger than object.Calculate the possible positions of objects.[Hint:MP=D/u=v/u]

Answer 1

Given -

Image size/ object size = 4

f = 20 cm

u = ?

Solution -

Magnification = Image size/ object size =4

But magnification = |v/u| = 4

i) When image is real and inverted,

-v/u = 4

v = -4u

1/f = 1/v - 1/u

1/20 = -1/4u - 1/u

1/20 = -5/4u

u = -25cm

Between the centre of the curvature and its focus, the image is real.

ii) When image is virtual and erect,

v/u = 4

v = 4u

1/f = 1/v - 1/u

1/20 = 1/4u - 1/u

1/20 = -3/4u

u = -15cm

Between focus and its optic centre, the image is virtual.

Hence two possible postions of object are -25cm and -15cm.