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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1 Answers

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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