Derive the formula for angle of deviation for thin prisms.ORShow that

1.	Derive the formula for angle of deviation for thin prisms.ORShow that in a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).
Answer» 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).

Derive the formula for angle of deviation for thin prisms.ORShow that in a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).

Answer»

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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Derive the formula for angle of deviation for thin prisms.ORShow that in a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).

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