A beam of white light is partially reflected and partially refracted from a surface. The angle between the…

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
  1. $70^{\circ}$
  2. $60^{\circ}$
  3. $55^{\circ}$
  4. $58^{\circ}$

Solution

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: $\therefore i=r=90^{\circ}-r_F=90^{\circ}-30^{\circ}=60^{\circ}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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