Question

Figure shows a ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, show that (i) r₁ = r₂ = A/2 and (ii) angle of minimum deviation, D_m = 2i − A.

Answer 1

(i) When QR is parallel to the base BC, we have: i = e

\[\Rightarrow r_1 = r_2 = r\]

We know that

\[r_1 + r_2 = A\]

\[ \Rightarrow r + r = A \]

\[ \therefore r = A/2\]

(ii) Also, we have:
A + D= i + e
Substituting, D = D_m and e = i
A + D_m= i + i
∴ D_m=2i - A