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Question
(i) A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of 30°. Calculate the speed of light through the prism.
(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.
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Solution
(i) μ = `sin((A + δ_m)/2)/(sin(A/2))`
= `(sin((60 + 30)/2))/(sin(60^circ/2))`
= `sqrt(2)`
Also μ = `c/v`
⇒ v = `(3 xx 10^8)/sqrt(2)` m/s
(ii)
At face AC, let the angle of incidence be r2. For grazing ray, e = 90°
⇒ μ = `1/sinr_2`
⇒ r2 = `sin^-1(1/sqrt(2))` = 45°
Let the angle of refraction at face AB be r1.
Now r1 + r2 = A
∴ r1 = A – r2 = 60º – 45º = 15º
Let the angle of incidence at this face be i
μ = `sini/sin r_1`
⇒ `sqrt(2) = sini/sin15^circ`
∴ i = `sin^-1 (sqrt(2).sin15^circ)` = 21.5º
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