A) \[30cm\]
B) \[20cm\]
C) \[10cm\]
D) \[90cm\]
Correct Answer: B
Solution :
: As radius of curvature \[(R)\] is negative for a concave mirror, so \[R=-30cm\] \[\therefore \]The focal length of the mirror is \[f=\frac{R}{2}=\frac{-30\,cm}{2}=-15cm\] As the person wants his real enlarged image, so magnification, \[m=-\frac{v}{u}=-3\] or \[v=3u\] According to mirror formula \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\] \[\therefore \] \[\frac{1}{3u}+\frac{1}{u}=\frac{1}{-15cm}\] \[\frac{1+3}{3u}=\frac{1}{-15cm}\] or \[\frac{4}{3u}=\frac{1}{-15cm}\] \[u=\frac{-60cm}{3}=-20cm\] \[-ve\] sign shows that the person should stand in front of the mirror.
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