For refraction through an equilateral glass prism, at minimum deviation \( (D_{m} = 30^{\circ}) \), which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \angle i+\angle r = 75^{\circ} \)
At minimum deviation the ray passes symmetrically through the prism: the two angles of refraction are equal, and the angle of incidence equals the angle of emergence.
\( r_{1} = r_{2} = r,\quad A = 2r,\quad A+D_{m} = 2i \)
For an equilateral prism, \( A = 60^{\circ} \), and \( D_{m} = 30^{\circ} \):
\( \displaystyle r = \frac{A}{2} = 30^{\circ} \)
\( \displaystyle i = \frac{A+D_{m}}{2} = \frac{60^{\circ}+30^{\circ}}{2} = 45^{\circ} \)
\( \angle i+\angle r = 45^{\circ}+30^{\circ} = 75^{\circ} \)