First slide

Ray optics

Question

A plane mirror is lying in xy-plane with its reflecting surface facing positive z-axis. A particle is moving towards the reflecting surface of the mirror with velocity $(2 \hat{i} - 2 \hat{j} - 3 \hat{k}) m / s$ . If the mirror starts moving with velocity $2 \hat{k} m / s$ , velocity of the image of the particle relative to the mirror is

Difficult

A

$(2 \hat{i} - 2 \hat{j} - 5 \hat{k}) m / s$
B

$(2 \hat{i} + 2 \hat{j} + 5 \hat{k}) m / s$
C

$(- 2 \hat{i} + 2 \hat{j} + 5 \hat{k}) m / s$
D

$(2 \hat{i} - 2 \hat{j} + 5 \hat{k}) m / s$

Solution

Velocity of the particle relative to the mirror is given by, ${\vec{V}}_{P / M} = {\vec{V}}_{P} - {\vec{V}}_{M} = (2 \hat{i} - 2 \hat{j} - 5 \hat{k}) m / s$
Therefore velocity of the image relative to the mirror is, ${\vec{V}}_{i / M} = (2 \hat{i} - 2 \hat{j} + 5 \hat{k}) m / s$ .

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