A man looks at his image in a concave mirror of 1m focal length by standing 3m away from it. Calculate the distance of the image of the man from the pole of the mirror. will the image formed be real or virtual? Also calculate the magnification, and find the image size and its nature.

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Solution

$D e a r S t u d e n t, G i v e n, f = - 1 m (F o c a l l e n g t h i s n e g a t i v e f o r a c o n c a v e m i r r o r .) u = - 3 m, v = ? W e k n o w, \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \Rightarrow - \frac{1}{1} = - \frac{1}{3} + \frac{1}{v} \Rightarrow \frac{1}{v} = - 1 + \frac{1}{3} = \frac{- 3 + 1}{3} = - \frac{2}{3} T h e r e f o r e, v = - \frac{3}{2} = - 1.5 m I m a g e i s f o r m e d a t 1.5 m a w a y f r o m t h e m i r r o r o n t h e s a m e s i d e a s t h e o b j e c t . A s' v' i s n e g a t i v e, i m a g e i s r e a l . (A l s o, i f m a g n i f i c a t i o n m i s n e g a t i v e, i m a g e i s r e a l) M a g n i f i c a t i o n, m = - \frac{v}{u} = - (\frac{- 1.5}{- 3}) = - 0.5 A l s o, m = \frac{h e i g h t o f t h e i m a g e (h_{i})}{h e i g h t o f t h e o b j e c t (h_{0})} \Rightarrow - 0.5 = \frac{h_{i}}{h_{0}} \Rightarrow h_{i} = - 0.5 h_{0} T h u s t h e i m a g e i s h a l f t h e s i z e o f t h e o b j e c t a n d a s m i s n e g a t i v e, i m a g e i s r e a l a n d i n v e r t e d . R e g a r d s$

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