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Question
A concave mirror has a focal length of 20 cm. Find the position or positions of an object for which the image-size is double of the object-size.
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Solution
Using sign conventions, given,
Focal length of the concave mirror:
f = −20 cm
As per the question,
Magnification (m) is:
\[m = - \frac{v}{u} = 2\]
⇒ v = −2u
Case I (Virtual image):
Using mirror formula,
\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow - \frac{1}{2u} - \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{3}{2u} = \frac{1}{f}\]
\[ \Rightarrow u = \frac{3f}{2} = 30 \text{ cm }\]
Hence, the required positions of objects are 10 cm or 30 cm from the concave mirror.
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