Question

The image formed by a spherical mirror is real inverted and is magnification -2 if the image is a distance of 30 from the mirror where is the object placed find focal length of the mirror

Answer 1

m= -v/u
-2 = -v/u
2= v/u
2u=v
 
but v = -30
thus u = -15

Answer 2

Answer:

Given :

Magnification m = - 2

Image distance v = 30 cm

We know :

m = - v / u

- 2 =  - (- 30 ) / u

u = - 15 cm

We have mirror formula :

1 / f = 1 / v + 1 / u

1 / f = 1 / - 15 - 1 / 30

1 / f = - 1 / 10

f = - 10 cm

When the object is moved 10 cm towards the mirror.

Then : u' = u - 10 cm

= > u' = - 5 cm

Again putting in formula to get v'

1 /  - 10 + 1 / 5 = 1 / v'

1 / v' = 2 - 1 / 10

v' = 10 cm

Therefore , the image is located 10 cm behind the mirror.

Also new magnification :

m' = -v' / u'

m' = - 10 / -5

m' = 2

Since magnification is positive the image is erect and virtual.

Also image is magnified in nature.