# You are given a concave mirror of focal length 50cm. How will you place an object in front of it, so that an image of double its size is obtained.

Sunil Bhardwaj

**Solution:** As we have a concave mirror focal length is negative, $$ \therefore f = -50 cm $$ and $$ Magnification (m) = \frac { v }{ u } = 2 $$ $$ \therefore v = 2u $$ By using mirror formula, $$ \frac { 1 }{ u } +\frac { 1 }{ v } =\frac { 1 }{ f } $$ Lets substitute the values, $$ \frac { 1 }{ u } +\frac { 1 }{ 2u } =\frac { 1 }{ -50 } \frac { 2+1 }{ 2u } $$ $$=\frac { -1 }{ 50 } \frac { 3 }{ 2u } $$ $$ =\frac { -1 }{ 50 } $$ $$ \therefore 2u = -\left( 3 \times 50 \right) $$ or $$ u = \frac { -150 }{ 2 } = -75 cm $$

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