Question

A concave mirror of focal length 20cm produces an image twice the height of an object .if the image is real ,then the distance of the object from the mirror is?

Answer 1

Hello Dear.

Here is the answer---

Given ⇒

Focal Length of the Mirror = 20 cm. (negative)

Let the Height of the Object be H.
∴ Height of the Image = 2H

Now, 
Magnification = H₁/H₀
 = 2H/H
 = 2

Also, m = -v/u
2 = -v/u
⇒  v = -2u

Now,
Image Distance = -2u 
Object distance = u
 
Using the Mirror Formula,

 $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
⇒ $\frac{1}{-20} = \frac{1}{-(-2u)} + \frac{1}{u}$
⇒ $\frac{1}{-20} = \frac{1 + 2}{2u}$
⇒ 2u = -20 × 3
⇒ 2u = -60
⇒ u = -30 cm.


∴ Distance of the Object from the mirror is 30 cm. Negative size shows that the object is kept on the side of the mirror.


Hope it helps.

Answer 2

Here two possibilities of answer can occur.