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Question

If a concave mirror has a focal length of 10 cm, find the two positions where an object can be placed to give, in each case, an image twice the height of the object.

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Solution

Given,
Focal length (f) of the concave mirror = -10 cm
Case-1
The image is real, and its magnification (m) is -2.
Using the magnification formula, we get
m=-vu-2 =-vu v=2u

Now, using the mirror formula, we get

1f =1v+1u1-10=12u+1u1-10=12u+22u=32u u =3×(-10)2=-15 cm The object should be placed at a distance of 15 cm from the concave mirror.

Case-2
The image is virtual and has a magnification 'm' of 2.
Using the magnification formula, we get

m=-vu

2 =-vu

v=-2u
Now, using the mirror formula, we get

1f=1v+1u

1-10=1-2u+1u

1-10=-12u+22u=12u u=-102=-5 cm

Thus, the object should be placed at a distance of 5 cm in front of the concave mirror.

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