Geometrical OpticsHard
Question
A ray of light passes through a prism in a principle plane the deviation being equal to of incidence which which is equal to 2α. It is given that α is the angle of prism and μ is the refractive index of the material of prism, then
Options
A.cos α = 
B.cos α = 
C.sin α = 
D.sin α = 
Solution
2α = (2α + e) - α
e = α, r1 + r2 = α
sin 2 α = μ sin r1,
μ sin (α - r1) = sin α
m (sin α.cos r1 - cos α sin r) = sin α
= sin α
sin α
- cos α sin 2 α = sin α
- 2 con2α = 1
μ2 = sin2 2α = 1 + 4 cos4 α + 4 cos2 α
μ2 = 1 + 4 cos4α + 4 cos2 α + 4 sin2 α cos2 α
μ2 = 1 + 4 cos2 α (sin2 α + cos2 α)
cos α =
e = α, r1 + r2 = α
sin 2 α = μ sin r1,
μ sin (α - r1) = sin α
m (sin α.cos r1 - cos α sin r) = sin α
= sin αsin α
- cos α sin 2 α = sin α - 2 con2α = 1μ2 = sin2 2α = 1 + 4 cos4 α + 4 cos2 α
μ2 = 1 + 4 cos4α + 4 cos2 α + 4 sin2 α cos2 α
μ2 = 1 + 4 cos2 α (sin2 α + cos2 α)
cos α =
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