question_answer

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 [NEET - 2018]

A)  30 cm towards the mirror

B)  36 cm away from the mirror

C)  30 cm away from the mirror

D)  36 cm towards the mirror

Correct Answer: B

Solution :

\[\frac{1}{f}=\frac{1}{{{v}_{1}}}+\frac{1}{u}\] \[-\frac{1}{15}=\frac{1}{{{v}_{1}}}-\frac{1}{40}\] \[\Rightarrow \frac{1}{{{v}_{1}}}=\frac{1}{-15}+\frac{1}{40}\] \[{{v}_{1}}=-24cm\] When object is displaced by 20 cm towards mirror. Now, \[{{u}_{2}}=-20\] \[\frac{1}{f}=\frac{1}{{{v}_{2}}}+\frac{1}{{{u}_{2}}}\] \[\frac{1}{-15}=\frac{1}{{{v}_{2}}}-\frac{1}{20}\] \[\frac{1}{{{v}_{2}}}=\frac{1}{20}-\frac{1}{15}\] \[{{v}_{2}}=-60cm\] So, image shifts away from mirror by\[=60-24=36cm\].