An object (O) and a plane mirror (M) are placed in the positions as shown in the figure. If the object and the mirror moves simultaneously towards right in a straight path at uniform speed of $2 c m s^{- 1}$ and $5 c m s^{- 1}$ respectively, find the shift in the image of the object at the end of 10 seconds :

40 c m

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80 c m

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20 c m

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60 c m

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Solution

The correct option is B $80 c m$
The effective speed with which the mirror will move away from the object will be $5 - 2 = 3$ cm/s
Hence, after $10$ s, mirror will be $30$ cm away from object. The mirror will be $50$ cm from its original position and the object $20$ cm.
The original image was formed $40$ cm on the right of the mirror. The new image will be formed $40 + 30 = 70$ cm on the right of the new position of the mirror
If O is origin,
Original position of object= $0$
Original position of mirror= $40$
Original position of image= $80$
New position of object= $20$
New position of mirror= $90$
New position of mage= $160$
Hence, shift in image= $160 - 80 = 80$ cm

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An object (O) and a plane mirror (M) are placed in the positions as shown in the figure. If the object and the mirror moves simultaneously towards right in a straight path at uniform speed of 2cms−1 and 5cms−1 respectively, find the shift in the image of the object at the end of 10 seconds :