First slide

Ray optics

Question

An object is placed on the principal axis of a concave mirror at a distance of 1.5 f (f is the focal length). The image will be at,

Easy

A

3 f
B

-3 f
C

1.5 f
D

-1.5 f

Solution

By mirror formula
$\begin{array}{l} \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \frac{1}{v} - \frac{1}{\frac{3 f}{2}} = \frac{1}{- f} \\ \frac{1}{v} - \frac{2}{3 f} = - \frac{1}{f} \\ \frac{1}{v} = - \frac{1}{f} + \frac{2}{3 f} \\ \frac{1}{v} = \frac{- 3 + 2}{3 f} \\ v = - 3 f \end{array}$

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