An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

30 cm away from the mirror

36 cm away from the mirror

36 cm towards the mirror

30 cm towards the mirror

Solution

36 cm away from the mirror

Using mirror formula,

$\frac{1}{f} = \frac{1}{v_{1}} + \frac{1}{u} - \frac{1}{15} = \frac{1}{v_{1}} + \frac{1}{u} \Rightarrow \frac{1}{v_{1}} = \frac{1}{- 15} + \frac{1}{40} ∴ = - 24 c m$

When object is displaced by 20 cm towards mirror Now,

u₂ = -20

So,

$\frac{1}{f} = \frac{1}{v_{2}} + \frac{1}{u_{2}} \frac{1}{- 15} = \frac{1}{v_{2}} - \frac{1}{20} \Rightarrow \frac{1}{v_{2}} = \frac{1}{20} - \frac{1}{15}$

Therefore, image shifts away from mirror by = 60-24 = 36 cm

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Ray Optics And Optical Instruments

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