A concave mirror of focal length 20cm and a convex lens of focal length 10cm are kept with their optic axis parallel but separated by 0.5 mm as shown in figure. The distance between lens and mirror is 10cm. An object of height 3 mm is placed on the optic axis of lens at distance 15 cm from the lens. Find height of image formed by mirror after refraction from lens (in mm).

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Detailed Solution

For image formed by lens $\frac{1}{v_{1}} - \frac{1}{- 15} = \frac{1}{100} \Rightarrow v_{1} = + 30 c m$
i.e. 20 cm behind mirror For mirror $\frac{1}{v_{2}} + \frac{1}{20} = \frac{1}{- 20} \Rightarrow v_{2} = - 10 c m$
Overall magnification $= (\frac{30}{- 15}) \times (\frac{10}{20}) = 1$
Length of image $= 1 \times 3 = 3$ mm

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