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Physics
The refracting angle of prism is A and refractive index of material of prism is cot (A/2) The angle of minimum deviation is
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Q. The refracting angle of prism is A and refractive index of material of prism is $\cot \frac{A}{2}$ The angle of minimum deviation is
KCET
KCET 2020
Ray Optics and Optical Instruments
A
$180^\circ -3 A$
11%
B
$180^\circ +2 A$
26%
C
$90^\circ - A$
16%
D
$180^\circ -2 A$
47%
Solution:
$n=\frac{\sin \left(\frac{A+d_{m}}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \cot \left(\frac{A}{2}\right)=\frac{\sin \left(\frac{A+d_{m}}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \frac{\cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}=\frac{\sin \left(\frac{A+d_{m}}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \sin \left(90-\frac{A}{2}\right)=\sin \left(\frac{A+d_{m}}{2}\right)$
$\Rightarrow 90-\frac{A}{2}=\frac{A+d_{m}}{2}$
$\Rightarrow 180-2 A=d_{m}$