Derive the formula for angle of deviation for thin prisms.
Derive the formula for angle of deviation for thin prisms.
OR
Show that in a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).
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For thin prisms (refracting angle < sin 10°).
sin θ ≈ θ
∴ Refractive index, n = \(\frac{sin\,i}{sin\,r_i}\) ≈ \(\frac{i}{r_1}\)
Also n = \(\frac{sin\,e}{sin\,r_2}\) ≈ \(\frac{e}{r_2}\)
∴ i ≈ n r1 and e ≈ nr2
ii. Substituting this in, i + e = A + δ,
we get,
i + e = n (r1 + r2) = nA = A + δ
∴ S = A(n – 1)
A and n are constant for a given prism.
Thus, for a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).
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