A ray of light is reflected by a plane mirror. e ^ 0 , e ^ and n ^ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively. Which of the following gives an expression for ê?

Question

A ray of light is reflected by a plane mirror. e ^ 0 ​ , e ^ and n ^ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively. Which of the following gives an expression for ê?, e ^ 0 ​ + 2 ( e ^ 0 ​ ⋅ n ^ ) n ^, e ^ 0 ​ − 2 ( e ^ 0 ​ ⋅ n ^ ) n ^, e ^ 0 ​ − ( θ ^ 0 ​ ⋅ n ^ ) n ^, $\mathrm{d}) \hat{\mathrm{e}}_{0}+\left(\hat{e}_{0} \cdot \hat{n}\right) \hat{\mathrm{n}$

MARKS App · Accepted Answer

(b) According to the question, We know that incident ray, reflected ray and normal lie in the same plane. and angle of incidence = angle of reflection Therefore n ^ will be along the angle bisector of e and − e ^ 0 ​ i.e. n ^ = ∣ e ^ − e ^ 0 ​ ∣ e ^ + ( − e ^ 0 ​ ) ​ [ ∵ Bisector will along a vector dividing in same ratio as the ratio of sides forming that angle ] But n ^ is a unit vector where ∣ e − e ^ 0 ​ ∣ = OC cos θ ​ = 20 P = 2∣ e ^ ∣ = 2 cos θ ​ Substituting this value in Eq. (i), we get n ^ = 2 c o s θ e ^ − e ^ 0 ​ ​ e ^ = e ^ 0 ​ + ( 2 cos θ ) n ^ e ^ = e ^ 0 ​ − 2 n ^ ⋅ e ^ 0 ​ ) n ^ [ ∵ n ^ ⋅ e ^ 0 ​ = − cos θ ] ​

Search any question & find its solution

Looking for more such questions to practice?