Question

Find the position of an object , which when placed in front of a concave mirror of focal length 10cm produces a virtual image , which is twice the size of the object.

Answer 1

Here,
h'=2h
where h is the object height and h' is the image height.
we know that,
             m=h'/h
but h'=2h
or  h'/h=2
so,m(magnification)=2
we know that m=h'/h=-v/u
where v is the image distance and u is the object distance.
so,   m=-v/u
or,    2=-v/u
or,    2u=(-v)..............................(eq.1)
by mirror formula,
1/f=1/v+1/u
or, 1/v+1/u=1/f
     1/v=1/f-1/u
      1/v=u-f/fu
or,   v=fu/u-f
          =u(-10)/u-(-10)
therefore,        v =(-10u)/u+10.......................(eq.2)
From eq.1,
              2u=(-v)
              2u=-[-10u/u+10]
                  =10u/u+10
              2u=10u/u+10
 or,          2u(u+10)=10u
 or,              u+10=10u/2u
 or,              u=5-10
 or,              u=(-5)
therefore,     object distance is 5 cm to the left side of the mirror.
SAY THANKS PLZ....