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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Ray Optics

NEET 2015 · Physics · Ray Optics

The refracting angle of a prism is A , and refractive index of the...

The refracting angle of a prism is AA , and refractive index of the material of the prism is cot⁡(A2)\cot \left(\dfrac{A}{2}\right). The angle of minimum deviation is

Options

  1. A180o−3A{180}^{o} - 3A
  2. B180o−2A{180}^{o} - 2A
  3. C900−A{90}^{0} - A
  4. D1800+2A{180}^{0} + 2A

Correct answer

B. 180o−2A{180}^{o} - 2A

Step-by-step solution

μ=sin⁡(\deltam+A2)sin⁡(A2)\mu = \dfrac{\sin \left(\dfrac{\deltam + A}{2}\right)}{\sin \left(\dfrac{A}{2}\right)}
∵μ=cot⁡(A2)∵ \mu = \cot \left(\dfrac{A}{2}\right)
∴cot⁡(A2)=sin⁡(\deltam+A2)sinA2∴ \cot \left(\dfrac{A}{2}\right) =\dfrac{\sin \left(\dfrac{\deltam + A}{2}\right)}{sin \dfrac{A}{2}}
cosA2=sin⁡(\deltam+A2)cos \dfrac{A}{2} = \sin \left(\dfrac{\deltam + A}{2}\right)
π2−A2=\deltam+A2\dfrac{\pi}{2} - \dfrac{A}{2} = \dfrac{\deltam + A}{2}
\deltam=π−2A\deltam = \pi - 2A
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