a convex mirror has a focal length of 18 cm . the image of an object kept in front of the mirror is half the height of the object . what isthe distance of the object from the mirror?

Hi Khushi Sinha, we can use mirror formula 1/f = 1/u + 1/v
By sign convention magnification m = image size / object size
So m = 1/2 * object size / object size = 1/2
Recall m = f /(f - u)
So 1/2 = 18 / (18 - u)
==> 18 - u = 36
OR - u =  18
Negative sign indicates that we measure object distance right from pole and opposite to the incident ray
So Distance of object in front of the mirror = 18 cm
Let us find the image distance too
Plug in 1/u + 1/v = 1/f
Here u = - 18 cm (by sign convention)
f =  + 18 cm
Plugging - 1/18 + 1/v = 1/18
==> 1/v = 2/18
OR v = 9 cm
Here is the related diagram

 
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HERE IS YOUR ANSWER
M = H2 = -V/U = 1/2
             = -V = U/2
         V = -4/2 
  1/V + 1/U = 1/F
  1/-U/2 + 1/U = 1/18
-2/U + 1/U  = 1/18
-U/U = 1/18
U = -18  
U = 18
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Please find this answer

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Given => f=18 cm, height of object(h) be cm , height of the image of object (h') =y/2 cm

m= h'/h =-v/u
So, y/2 ?1/y = -v/u

.?., 1/2 = -v/u
-u/2 = v

?.? 1/v+ 1/u= 1/f
=> -2/u + (-1/u) = 1/18
-3/u= 1/18
So, distance of the object from the mirror will be -54cm

Hope it will be helpful to you ??????
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