Question

A plane mirror is placed in y-z plane facing towards negative x-axis. The mirror is moving parallel to y-axis with the speed of 2 cm/s. A point object P is moving infront of the mirror with a velocity $\left(1cm/s\right)\hat{i})+(1cm/s)\hat{j}$. Then which of the following statements is incorrect?

• A. The velocity of image is $(\hat{i}+\hat{j})$ cm/s
• B. The velocity of image with respect to mirror is $(-\hat{i}+\hat{j})$ cm/s
• C. The velocity of image with respect to object is $(-2\hat{i})$ cm/s
• D. The unit vector in the direction of reflected ray is $\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Answer 1

The correct option is D The unit vector in the direction of reflected ray is $\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

The velocity of image,
For x-axis,
$v_x=2v_m-v_0=-\hat{i}$
For y-axis,
$v_y=v_0=\hat{j}$
thus, ${\overrightarrow{v}}_i=-\hat{i}+\hat{j}$

Velocity of image with respect to mirror,
${\overrightarrow{v}}_{im}={\overrightarrow{v}}_i-{\overrightarrow{v}}_m=(-\hat{i}+\hat{j})-2\hat{j}=(-\hat{i}-\hat{j})cm/s$
Velocity of image with respect to object
${\overrightarrow{v}}_i-{\overrightarrow{v}}_0=(-\hat{i}+\hat{j})-(\hat{i}+\hat{j})=-2\hat{i}cm/s$
Unit vector in the direction of reflected ray $\frac{(-\hat{i}+\hat{j})}{\sqrt{2}}$.