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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. - Physics

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ConceptDispersion by a Prism

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, Dm = 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 = Dand e = i
A + Dm= i + i
∴ Dm=2i - A

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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.
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