An object is placed at a distance of one and a half of the focal length of a concave mirror. Find the position of image in terms of 'f'. Also find the magnification and nature of image formed by a concave mirror.

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Solution

it is stated clearly object is at one and half of focal length of concave mirror,

so, let object distance u=(1+1/2)focal lenght(f)
=3/2f

u=-3f/2 after sign conventions
v=?
f=-f
by mirror formula:
1/f=1/v+1/u
1/v=1/f-1/u
=-1/f+2/3f
=(-3+2)/3f
=-1/3f
v=-3f image is beyond C
thus, m=-v/u=+3f/(-3f/2)=-2
m=-2
image is real, inverted and magnified

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