Question

The image formed by a spherical mirror is real, inverted and is of magnification- 2. If the image is at a distance of 30 cm from the mirror, where is the object placed .7 Find the focal length of the mirror List two characteristics of the image formed if the object is moved 10 cm towards the mirror.

Answer 1

v=- 60cm

f=-2cm

m=-2cm

u=-30cm

m=-v/u

-2=-v/-30

v=-60cm

now,1/f =1/v +1/u

1/f =-30-60/180

f=-2cm

Now,if object is moved 10cm towards mirror,it will form real and inverted image.Also,it will form a diminished image

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.