Question

A spherical concave mirror produces an image behind it, twice as large as the object at a distance of 8cm from its pole. Find the focal length and the type of the image?
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Answer 1

Answer:

Case 1 :

Magnification  m=−2   (image is real)

Object distance  u=−22.5cm

From  m=u−v

∴   −2=u−v

We get v=2u=−45cm

Using  f1=v1+u1

f1=−451−22.51=45−1−2

f1=45−3

⟹ f=−15cm

Case 2 :

Let the new object distance be x  i.e. u=−x now.

Magnification  m=−3   (image is real)

From  m=u−v

∴   −3=−x−v      ⟹v=−3x

Using  f1=v1