Q. Find the position of an object which when placed in front of a concave mirror of focal length 20cm produces a virtual image, which is twice the size of the object.
Answer→ 10cm
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Concave mirror :
Here,
Focal length of the mirror(f) = -20cm.
Magnification (m) = 2.
Object distance (u) = ?
We know that ,
m = -v/u.
2 = -v/u.
v = -2u.
Putting this value in mirror formula :
1/f = 1/v + 1/u.
1/-20 = 1/v + 1/u.
-1/20 = 1/-2u + 1/u.
(putting v = -2u ).
-1/20 = -1/2u + 1/u.
-1/20 = (-1 +2)/2u .
( LCM of 2u and u is 2u ).
-1/20 = 1/2u.
-1 × 2u = 1 × 20.
(Cross multiplication)
-2u = 20.
Therefore , u = -10.
So, the object should be placed at 10 cm in front of the mirror to obtain a virtual image two times the size of the object.
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