Question

An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 m from the optical centre of the lens. Find the nature, position and size of the image formed. Which case of image formation by convex lenses is illustrated by this example?

Answer 1

Given:
Size of object, h = 2 cm
Focal length, f = 5 cm
Object distance, u = $-$10 m = $-$1000 cm
Applying lens formula, we get:
1/v $-$ 1/u = 1/f
1/v = 1/f + 1/u
or, 1/v = 1/5 + 1/($-$1000)
or, 1/v=(-200+1)/-1000
or, 1/v=199/1000
or, 1/v=1000/199
or, v=5 cm (approx)
Image distance, v =5 cm behind the lens;

Applying magnification formula, we get:

m = h'/h = v/u
m = h'/2 = (5)/($-$1000)

or, h' = $-$0.01 cm

Thus, the size of the image is 0.01 cm.
So, the image is inverted (h' is negative), highly diminished (h' is smaller than h) and real (v is positive).

Therefore, from the above results we conclude that:
When an object is placed beyond 2f, the image is real, inverted and diminished and is formed between f and 2f.