Question

a concave mirror forms a real image three times larger than the object on a screen the object and screen are moved until the image becomes twice the size of the shift of screen

Answer 1

The mirror produces three times enlarged image.

So, magnification(m) = 3

WE KNOW, magnification of spherical mirrors = m = -v/u

Where v is the distance between image and mirror and u is the distance between object and mirror.

Here, u = -10 cm

=> 3 = -V/-10

=>v = 30

So , the distance between image and mirror = 30 cm

1/v + 1/u = 1/f(mirror formula)

1/30 + 1/-10 = 1/f

1/30 - 1/10 = 1/f

-2/30 = 1/f

-1/15 = 1/f

f = -15 cm

We know radius of curvature = 2f

So, radius of curvature = R = 2*-15 = -30 cm which is the required answer.

SHORTCUT -

Remember the formula, m = f/(f-u)

So, 3 = f/(f-(-10))

3 = f/(f+10)

Cross multiply,

3f + 30 = f

2f = -30

R = -30 cm (R= 2f).