An object is placed at a distance of 30 cm from a concave mirror of focal length 10 cm. If the object is displaced through a distance of 10 cm towards the mirror, the displacement of the image will be?

Question

Answer

Given:

Distance of object from concave mirror, u = 30 cm

Focal length of mirror, f = -10 cm (negative sign indicates concave mirror)

Displacement of object, δu = 10 cm

Formula:

Mirror formula: 1/f = 1/v - 1/u

Magnification formula: m = -v/u

Displacement formula: δv = m x δu

Solution:

Using the mirror formula:
1/f = 1/v - 1/u

1/-10 = 1/v - 1/30

1/v = 1/-10 + 1/30 = -1/15

v = -15 cm

Using the magnification formula:
m = -v/u

m = -(-15)/30 = 0.5

Using the displacement formula:
δv = m x δu

δv = 0.5 x 10 = 5 cm

Answer:
The displacement of the image will be 5 cm. When the object is displaced through a distance of 10 cm towards the mirror, the image is also displaced towards the mirror but by a smaller distance of 5 cm.

Answer

Given ui=-30cm,fi=-10cm
1/vi+1/ui=1/f
1/vi+1/-30=1/-10
vi=-15cm
finally uf=-10cm f=-10cm
1/vf+1/uf=1/f
1/vf+1/-10=1/-15
Vf=-30cm
image shifted by 30-15=15cm away from the mirror
Although not sure is it correct or not???

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