An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm . If the obje

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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\

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(b)\ Using mirror formula,\ $\frac{1}{f}=\frac{1}{v_{1}}+\frac{1}{u_{1}} ;-\frac{1}{15}=\frac{1}{v_{1}}-\frac{1}{40} \Rightarrow \frac{1}{v_{1}}=\frac{1}{-15}+\frac{1}{40}$\ $v_{1}=-24 \mathrm{~cm}$\ When object is displaced by 20 cm towards mirror. Now, $u_{2}=$ $-20 \mathrm{~cm}$\ $\frac{1}{f}=\frac{1}{v_{2}}+\frac{1}{u_{2}} ; \frac{1}{-15}=\frac{1}{v_{2}}-\frac{1}{20} \Rightarrow \frac{1}{v_{2}}=\frac{1}{20}-\frac{1}{15}$;\ $v_{2}=-60 \mathrm{~cm}$\ So, the image will be shift away from mirror by\ $(60-24) \mathrm{cm}=36 \mathrm{~cm}$.\