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Question
A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?
Solution
Given,
Distance between the convex lens and the convex mirror is 15 cm.
The focal length (f1) of the lens is 25 cm.
The focal length (f2) of the mirror is 40 cm.
Let x cm be the object distance from the mirror.
Therefore,
u = − x cm
v = 25 − 15 = + 10 cm (∵ focal length of lens = 25 cm)
∴ f1 = + 40 cm
Using lens formula:
\[\Rightarrow \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\Rightarrow\frac{1}{x}=\frac{1}{10}-\frac{1}{40}\Rightarrow x=\frac{400}{30} = \frac{40}{3}\]
Thus, the object distance is \[\left( 15 - \frac{40}{3} \right)=\frac{5}{3}\]
= 1.67 cm from the lens
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