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A beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is $90^{\circ}$. The angle of refraction is $30^{\circ}$. The angle of incidence must be
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Verified Answer
The correct answer is:
$60^{\circ}$
Consider the following figure:
Take angle of incidence $i$, angle of reflection $r$ and angle of refraction
$r_{\mathrm{F}}=30^{\circ}$
Given from geometry:
$\begin{aligned}
& r+r_{\mathrm{F}}+90^{\circ}=180^{\circ} \\
& \Rightarrow r=90^{\circ}-r_{\mathrm{F}}
\end{aligned}$
Since, angle of incidence is equal to the angle of reflection:
$\therefore i=r=90^{\circ}-r_F=90^{\circ}-30^{\circ}=60^{\circ}$
Take angle of incidence $i$, angle of reflection $r$ and angle of refraction
$r_{\mathrm{F}}=30^{\circ}$
Given from geometry:
$\begin{aligned}
& r+r_{\mathrm{F}}+90^{\circ}=180^{\circ} \\
& \Rightarrow r=90^{\circ}-r_{\mathrm{F}}
\end{aligned}$
Since, angle of incidence is equal to the angle of reflection:
$\therefore i=r=90^{\circ}-r_F=90^{\circ}-30^{\circ}=60^{\circ}$
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