For an equilateral prism where the angle of prism
A is equal to
60∘, when the light undergoes minimum deviation, the angle of incidence
(i) becomes equal to the angle of emergence
(e) and both are equal to the angle of prism divided by 2 , i.e.,
i=e=‌.
In this question, it is given that the angle of incidence is
‌×A. When the light undergoes minimum deviation, for an equilateral prism,
‌=‌×A. Solving for
A :
‌‌=‌‌‌=‌This equation is incorrect, based on the information about minimum deviation. But for solving the refraction through a prism at minimum deviation and relating it to the velocity of light in the prism:
We use Snell's Law and the formula for refractive index. The refractive index
n of the glass can be given by:
n=‌At minimum deviation,
i=e=‌ and the deviation
δ is minimum. For an equilateral prism where
A=60∘ :
n=‌ sin‌(30∘)=0.5Since the angle of incidence is
‌A=‌×60∘=45∘, and given that this is minimum deviation, let's skip forward with using the fact that it achieves symmetry at minimum deviation, we simplify calculations by using the angle condition:
From Snell's law at air-glass interface:
‌sin‌(i)=nsin‌(r)‌sin‌(45∘)=nsin‌(30∘)‌‌=n×0.5‌n=‌=√2 The velocity of light in the glass prism,
v, is related to the velocity in vacuum,
c, by the refractive index:
v=‌Given that
n=√2 :
v=‌Thus, the answer is Option D:
‌