Concept:When the refracted ray inside a prism is parallel to its base, the prism is at the position of minimum deviation. For an equilateral prism, the angle of the prism (
A) is
60∘.
Formula:At minimum deviation: Angle of incidence equals angle of emergence (
i=e).
Prism formula:
i+e=A+δ, where
δ is the angle of deviation.
So,
δ=2i−A.
Solution:Given:
i=50∘,
A=60∘ (equilateral prism).
Since
QR∥BC, the prism is at minimum deviation, thus
i=e.
Using
δ=2i−A:
δ=2(50)−60=100−60=40∘.
Therefore, the angle of deviation is
40∘.
Shortcut:For an equilateral prism at minimum deviation,
δ=2i−60∘. Directly substitute
i=50∘ to get
δ=40∘.
Answer:C.
40∘