Question

The angle of deviation $\psi$ of a reflected light from the incident light($\theta$) is

• A. $\theta$
• B. $2\theta$
• C. $180-\theta$
• D. $180-2\theta$

Answer 1

Answer: (D)

$180-2\theta$

$\begin{array}{c}\text{angle of incidence}=\theta \\ \text{angle of reflechon also}=\theta \\ (\angle i=\angle \gamma )\\ \angle AO{x}^{\prime }+\angle i+\angle \gamma +\angle BOX=180\end{array}$

(angle in straight line)

$\Rightarrow \angle AO{x}^{\prime }+\angle BOX+\theta +\theta =180$

but $\angle AO{x}^{\prime }=\angle BO\times$ (both equal to $(90-\theta )$

$\Rightarrow \angle AO{x}^{\prime }+\angle AO{X}^{\prime }=180-2\theta$

$\Rightarrow$ Or,

$\angle AO{x}^{\prime }+\angle BOX=180-2\theta$

$\angle AO{x}^{\prime }=\angle \mathrm{cox}($ vertically opposite angle) $\Rightarrow \therefore \angle COx+\angle BOX=180-2\theta$

$\Rightarrow \angle BOC=180-2\theta$

$\varphi =180-2\theta$ (deviation angle)

$\therefore$ Option (D) is correct