Question

the image formed by a spherical mirror is real, inverted and is of magnification - 2. if the imageis at a distance of 30 cm from the mirror, where is the object placed? find the focal length of the mirror

Answer 1

Magnification = -v/u
Given that v= -30cm
-(-30)/u= -2
u= -15
1/f=1/v+1/u
1/f=1/-30-1/-15
1/f= -3/30
1/f=-1/10
Focal length= -10cm.

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.