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 middle where is the object placed ? find the focal length of the Middle East two characteristic of the image formed if the object is 10 centimetre toward the mirror

Answer 1

Hey dear,

● Answer-
u = -15 cm
f = 10 cm

● Explaination-
# Given-
v = 30 cm
M = -2

# Solution-
Maginification is given by-
M = v/u
u = v/M
u = -30/2
u = -15 cm

The object is placed 15 cm in from optical centre.

Focal length of mirror,
1/f = 1/v - 1/u
1/f = 1/30 + 1/15
1/f = 1/10
f = 10 cm

Focal length of mirror is 10 cm.

Hope this is useful...

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.