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WBJEE · Physics · Ray Optics

A ray of light is reflected by a plane mirror. \(\hat{e}_{0}, \hat{e}\) and \(\hat{n}\) 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?

  1. A \(\hat{e}_{0}+2\left(\hat{e}_{0} \cdot \hat{n}\right) \hat{n}\)
  2. B \(\hat{\boldsymbol{e}}_{0}-2\left(\hat{\boldsymbol{e}}_{0} \cdot \hat{\mathbf{n}}\right) \hat{\mathbf{n}}\)
  3. C \(\hat{\mathbf{e}}_{0}-\left(\hat{\boldsymbol{\theta}}_{0} \cdot \hat{\mathbf{n}}\right) \hat{\mathbf{n}}\)
  4. D \(\mathrm{d}) \hat{\mathrm{e}}_{0}+\left(\hat{e}_{0} \cdot \hat{n}\right) \hat{\mathrm{n}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\hat{\boldsymbol{e}}_{0}-2\left(\hat{\boldsymbol{e}}_{0} \cdot \hat{\mathbf{n}}\right) \hat{\mathbf{n}}\)

Step-by-step Solution

Detailed explanation

\(\text { (b) According to the question, }\) We know that incident ray, reflected ray and normal lie in the same plane. and angle of incidence \(=\) angle of reflection Therefore \(\hat{\mathrm{n}}\) will be along the angle bisector of e and \(-\hat{e}_{0}\) i.e.…