Question

At what distance from a concave mirror of focal length 3m should a boy stand so
that his image is half his height?​

Answer 1

$\huge\sf{\underline{\underline{➪Sᴏʟᴜᴛɪᴏɴ \: :-}}}$

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:

➪Sᴏʟᴜᴛɪᴏɴ:−

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