Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is ______ ×10−10s. (Given, speed of light in vacuum =3×108m/s and cos30∘=23)
Answer: 5
Solution
At minimum deviation of an equilateral prism the angle of incidence equals the prism angle, i=A=60∘, and the refracted ray runs parallel to the base, so r=A/2=30∘. The refractive index is
n=sinrsini=sin30∘sin60∘=3.
With side 10 cm, the distance from P (midpoint of BC) to A is the altitude PA=23(10)=53cm=0.053m. Inside the prism light travels at v=c/n, so
t=c/nPA=cPAn=3×108(0.053)(3)=5×10−10s.
The time taken is 5×10−10 s.
JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Integer answer
