A ray is reflected in turn by three plane mir | vedclass

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(C) Let the incident ray be represented by the vector $\vec{v} = (l, m, n)$,where $l^2 + m^2 + n^2 = 1$.When a ray reflects off a mirror perpendicular

Vedclass · Accepted Answer

$180$

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(C) Let the incident ray be represented by the vector $\vec{v} = (l, m, n)$,where $l^2 + m^2 + n^2 = 1$.When a ray reflects off a mirror perpendicular to the $x$-axis,the $x$-component of the velocity vector reverses sign: $(l, m, n) ightarrow (-l, m, n)$.After reflection from three mutually perpendicular mirrors (perpendicular to the $x, y,$ and $z$ axes respectively),the final direction of the ray becomes $(-l, -m, -n) = -\vec{v}$.The angle $	heta$ between the incident ray $\vec{v}$ and the reflected ray $-\vec{v}$ is given by $\cos 	heta = \frac{\vec{v} \cdot (-\vec{v})}{ |\vec{v}| |-\vec{v}| } = -1$.Thus,$	heta = 180^o$.Therefore,the ray becomes anti-parallel to the incident ray.

$A$ ray is reflected in turn by three plane mirrors mutually at right angles to each other. The angle between the incident and the reflected rays is......$^o$

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