A trihedral prism with refracting angle 6 0 ∘ deviates a light ray by 3 0 ∘ . The refractive index of the material of prism

δ m i n ≤ 3 0 ∘ gives μ = s i n 3 0 ∘ s i n 2 6 0 ∘ + δ m i n ≤ s i n 3 0 ∘ s i n 4 5 ∘ = 2 For the lower bound use the grazing-emergence limit: r 2 = C with sin C = μ 1 and r 1 = 6 0 ∘ − C ; the limiting case r 1 → 0 gives sin C = sin 6 0 ∘ , i.e. μ = 3 2 . Hence 3 2 ≤ μ ≤ 2 : (A) and (B) are true.

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Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsTIR/Prism and DispersionMedium2 minQB

PhysicsMediummultiple choice

A trihedral prism with refracting angle $6 0^{\circ}$ deviates a light ray by $3 0^{\circ}$ . The refractive index of the material of prism

Options:(select one or more)

Answer:

A, B

Solution:

$δ_{m i n} \leq 3 0^{\circ}$ gives $μ = \frac{s i n \frac{6 0 ^{\circ} + δ _{m i n}}{2}}{s i n 3 0 ^{\circ}} \leq \frac{s i n 4 5 ^{\circ}}{s i n 3 0 ^{\circ}} = 2$

For the lower bound use the grazing-emergence limit: $r_{2} = C$ with $sin C = \frac{1}{μ}$ and $r_{1} = 6 0^{\circ} - C$ ; the limiting case $r_{1} \to 0$ gives $sin C = sin 6 0^{\circ}$ , i.e. $μ = \frac{2}{3}$ .

Hence $\frac{2}{3} \leq μ \leq 2$ : (A) and (B) are true.

Stream:JEESubject:PhysicsTopic:Geometrical OpticsSubtopic:TIR/Prism and Dispersion

⏱ 2mℹ️ Source: QB

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