Question

at what distance from a concave mirror of focal length 2m should a boy stand so that his image is half his height

Answer 1

Given,
focal length= 2m = 200cm
let, height of boy be x
therfore, height of image = x/2

magnification = height of image/height of object
= x/2/x
= x/2 × 1/x
magnification= 1/2 = 0.5
sorry, i'cany

Answer 2

Given,

The focal length of the concave mirror = 2m.

To Find,

Distance to Image.

Solution,

We can solve this mathematical problem using mathematical formulas.

Magnification = $\frac{Height of the image}{Height of the object}$ = - $\frac{Image distance }{Object distance}$

Let the actual height be x

⇒$\frac{(\frac{x}{2}) }{x}$

⇒$\frac{1}{2}$ = - $\frac{v}{u}$

Using sign conversation,

$\frac{1}{2}$ = $\frac{v}{u}$

u = 2v

That is the object distance is twice the image distance.

So, the object should be placed at the center of the curved and the image will be formed at focus.

The object should be placed at the center of curvature 2(2)= 4 cm.

The image will be formed at focus = 2cm.