Question

Assertion: The right-handed coordinate system is converted into a left-handed coordinate system by a plane mirror.
Reason: Plane mirror produces the reversal in the direction of normal.

A) Both Assertion and Reason are correct and Reason the correct explanation for Assertion
B) Both assertion and Reason are correct but Reason is not the correct explanation for Assertion
C) Assertion is correct but the reason is incorrect
D) Assertion is incorrect but Reason is correct

Answer 1

Hint : The axis normal to the mirror will be flipped in the reflection of the right-hand coordinate system. The plane mirror reverses the direction of the axis that is normal to the surface of the plane mirror.

Complete step by step answer
When a coordinate system is placed in front of a mirror, we know that the mirror will flip the direction of the axis that is pointing towards the mirror. This can be seen in the real world where if we were to stand in front of the mirror and extend our arm towards the mirror i.e. away from us, in the mirror the arm extended by our image will have the opposite direction, and the arm will be extended towards us which implies that the direction of coordinate axis in the direction of our arm is reversed.
So, the assertion that the right-handed coordinate system will turn into a left-handed coordinate system is correct as the axis that is facing towards the mirror i.e. the $ x $ -axis will be flipped in the image. So the direction of the $ x' $ -axis will be in the direction opposite to the $ x $ -axis so the new coordinate system is left-handed as the $ x' $ -axis is on the left side. The reason provided for the assertion is also correct since the direction of the axis that is reversed i.e the $ x $ -axis is normal to the surface of the mirror. And the flipping of $ x $ -axis is why the right-handed coordinate system will turn into a left-handed coordinate system.
Hence the correct choice is option (A).

Note
It is helpful in such questions to use real-life examples to test the assertion given in the question by imagining a person standing in front of the mirror and checking the nature of the image that is formed. The reason provided is only correct for the reversal of direction of the axis normal to the mirror and not for any other axis since the other two axes remain unchanged in the reflection as they are parallel to the surface of the mirror.