Question

The maximum refractive index of a prism which permits the passage of light through it when the refracting angle of the prism is 90

Answer 1

The value of refractive index is μ(max) > √2

Step-by-step explanation:

A > 2θc

90 > 2θc

θc < 45°

1/μ < 1/√2

μ=cos(A/2)

μ=cos(90/2)

μ < √2

μ(max) > √2

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Answer 2

$\bold {Maximum\ Refractive\ Index\ of\ the\ prism\ = \sqrt{2}}$

Explaination:

A(Angle of prism) = 90° [Apex Angle]

$\delta_m_i_n = 0$ [Anlge of deviation]

Now,

$\mu =\frac{sin(A+\delta_m_i_n)}{sin(\frac{A}{2})}$

$\mu = \frac{sin(90+0)}{sin(45)}$

$\mu = \frac{sin(90)}{sin(45)}$

$\mu = \frac{1}{\frac{1}{\sqrt 2}}$

$\bold{\mu = \sqrt 2}$

$\bold{Hence,\ the\ maximum\ of\ refractive\ index\ is\ \sqrt 2}$