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Question
A 1 cm object is placed perpendicular to the principal axis of a convex mirror of focal length 7.5 cm. Find its distance from the mirror if the image formed is 0.6 cm in size.
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Solution
Given,
Height of the object, h1 = 1 cm
Focal length of the concave mirror, f = 7.5 cm = \[\frac{15}{2} \text { cm }\]
Magnification is given as,
\[m = - \frac{v}{u} = \frac{h_i}{h_0} = 0 . 6 \]
\[\text{ Using mirror equation,} \]
\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{1}{0 . 6u} - \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{5}{3u} - \frac{1}{u} = \frac{2}{15}\]
\[ \Rightarrow u = 5 \text{ cm }\]
Hence, the distance of the object from the mirror is 5 cm.
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