A light ray in free space is described by the incident vector and strikes a plane…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Geometric Optics · Geometric Optics

Problem

A light ray in free space is described by the incident vector

\mathbf{I}

and strikes a plane mirror whose outward unit normal is

\mathbf{n}

. (i) Derive an expression for the reflected vector

\mathbf{R}

in terms of

\mathbf{I}

and

\mathbf{n}

. (ii) Using the expression obtained in part (i), determine

\mathbf{R}

when

\mathbf{I}=2\hat{\imath}+\hat{\jmath}-2\hat{k}

and

\mathbf{n}=\dfrac{1}{\sqrt{3}}(\hat{\imath}+\hat{\jmath}+\hat{k})

. (iii) Verify explicitly that the angles of incidence and reflection are equal for the numerical vectors of part (ii).