#### 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) *r*_{1} = *r*_{2} = A/2 and (ii) angle of minimum deviation, D_{m} = 2i − A.

#### Solution

(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

Is there an error in this question or solution?

Solution 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, Dm = 2i − A. Concept: Dispersion by a Prism.