A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index

Question

A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index (A) 2 cos -1((μ/2)) (B)  sin -1((μ/2)) (C)  sin -1(√(μ-1/2)) (D)  cos -1((μ/2))

Tardigrade Admin · Accepted Answer

μ=( sin ((A+δ min /2))/ sin ((A)2)) μ=( sin ((A+A/2))/ sin ((A)2)) μ=( sin A/ sin (A)2)=2 cos (A/2) A=2 cos -1((μ/2))

Q. A prism of refractive index $μ$ and angle of prism $A$ is placed in the position of minimum angle of deviation. If minimum angle of deviation is also $A$ , then in terms of refractive index

$2 cos^{- 1} (\frac{μ}{2})$

$sin^{- 1} (\frac{μ}{2})$

$sin^{- 1} (\frac{μ - 1}{2})$

$cos^{- 1} (\frac{μ}{2})$

$μ = \frac{s i n ( \frac{A + δ _{m i n}}{2} )}{s i n ( \frac{A}{2} )}$
$μ = \frac{s i n ( \frac{A + A}{2} )}{s i n ( \frac{A}{2} )}$
$μ = \frac{s i n A}{s i n \frac{A}{2}} = 2 cos \frac{A}{2}$
$A = 2 cos^{- 1} (\frac{μ}{2})$

Q. A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index

2cos−1(2μ​)

sin−1(2μ​)

sin−1(2μ−1​​)

cos−1(2μ​)