Question

At what distance from a Convex lens of focal length 2.5 m should Rohan stand so that his image is half his height.

Answer 1

Explanation:

Magnification=height of the image/height of the object = -image distance/object distance

Let the actual height be x

=(x/2)/x

=1/2

1/2= -v/u

Using sign convention,

1/2 = v/u

u=2v

That is object distance is twice the image distance

So, the object should be placed at the centre of curvature and the image will be formed at focus.

Object should be placed at centre of curvature =2(2.5)=5cm

The image will be formed at focus =2.5cm

Answer 2

Answer:

Rohan should stand at 7.5m from the convex lens so that his image is half his height.

Explanation:

Data: Convex lens, f=2.5m, M= -1/2.

u=?

M= -1/2=v/u

∴ v= -u/2

1/f=1/v - 1/u=1/(-u/2) - 1/u= -2/u -1/u = -3/u

∴ u=-3f = -3×2.5 = -7.5m

This is the object distance.