question_answer

A plane mirror is moved away from a stationary object with a speed of 20 cm/s. What is the speed of the image?

Answer:

The speed of image = \[\frac{Distance\text{ }travelled\text{ }by\text{ }image}{Time}\] Let us consider that the mirror has moved for 1 second. \[\Rightarrow \]The distance travelled by mirror\[=20\text{ }cm/s\] Let the initial distance between object and mirror be\[x\]. From the figure, it is clear that \[OM=x\]            \[\Rightarrow \] \[MI=x\] Let M be the final position of the mirror. \[\Rightarrow \]New object distance\[=OM=(x+20)cm\] \[\Rightarrow \]New image distance\[=MI=(x+20)cm\] The distance moved by the image II \[=MIMI=20+x\text{ }20x=40\text{ }cm\] \[\Rightarrow \]Speed of image\[=\frac{40}{1}=40\,cm/s\]