Verified Solution • 2025–26 Session moderate

QJEEM24Ph272d: JEE Main 2024 Physics - Class 12 JEEM24Ph272d Solution: If the refractive index of the material of a prism is , where…

If the refractive index of the material of a prism is cot⁡(A2)\cot \left(\frac{A}{2}\right) , where AA is the angle of prism then the angle of minimum deviation will be

Multiple Choice Options

  • A π−2 A\pi-2 \mathrm{~A}
  • B π2−2 A\frac{\pi}{2}-2 \mathrm{~A}
  • C π−A\pi-\mathrm{A}
  • D π2−A\frac{\pi}{2}-\mathrm{A}

Step-by-Step Verified Solution

amp;cot⁡A2=sin⁡(A+δmin⁡2)sin⁡A2amp;⇒cos⁡A2=sin⁡(A+δmin⁡2)amp;A+δmin⁡2=π2−A2amp;δmin⁡=π−2 A\begin{aligned}& \cot \frac{\mathrm{A}}{2}=\frac{\sin \left(\frac{\mathrm{A}+\delta_{\min }}{2}\right)}{\sin \frac{\mathrm{A}}{2}} \\& \Rightarrow \cos \frac{\mathrm{A}}{2}=\sin \left(\frac{\mathrm{A}+\delta_{\min }}{2}\right) \\& \frac{\mathrm{A}+\delta_{\min }}{2}=\frac{\pi}{2}-\frac{\mathrm{A}}{2} \\& \delta_{\min }=\pi-2 \mathrm{~A}\end{aligned}%

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