1. Prism.
2. Refraction through a prism:
ABC is a section of a prism. AB and AC are the refracting faces, BC is the base of the prism. ∠A is the angle of prism. Aray PQ incidents on the face AB at an angle i_{1} . QR is the refracted ray inside the prism, which makes two angles r_{1} and r_{2} (inside the prism). RS is the emergent ray at angle i_{2} .
The angle between the emergent ray and incident ray is the deviation ‘d’. In the quadrilateral AQMR,
∠A + ∠R = 180°
[since N_{1} M are normal]
ie, ∠A + ∠M = 180°..........(1)
In the ∆ QMR,
∴ r_{1} + r_{2} + ∠M = 180° ...... (2)
Comparing eq (1) and eq (2)
r_{1} + r_{2} = ∠A ......(3)
From the ∆ QRT,
(i_{1} – r_{1}) + (i_{2} – r_{2}) = d
[since exterior angle equal sum of the opposite interior angles]
(i_{1} + i_{2}) – (r_{1} + r_{2}) = d
but, r_{1} + r_{2} = A
∴ (i_{1} + i_{2}) – A = d
3. At minimum deviation D = 2i – A, r_{1} = r_{2} = r
i = \(\frac{A+D}{2},r = \frac{A}{2}\)
n = \(\frac{sin\,i}{sin\,r}\) = \(Sin\frac{A+D}{\frac{2}{Sin\frac{A}{2}}}\)
4. Deviation decreases.