# Size of image of an object by a mirror having focal length of 20cm is observed to be reduced to 1/3rd of its size. At what distance tthe object has been placed from the mirror? What is the nature and size?

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As specific denotion

h2=1/3 h1

h2/h1=1/3=m

as we know that m=-v/u=1/3

v=-1/3u

applied mirror formula

1/f=1/v+1/u

1/-20=-3u/1+1/u

-1/20=-3u^2+1 whole divided by u

cross multiply

-u=-60u^2+20

60u^2-u-20=0

solve quartic equation

u=71/120,u=69/120

u=0.59 and u=0.57