Question

Two beams of red and violet colour are made to pass separately through a prism with angle of prism $60^{\circ}$. In the position of minimum deviation, the angle of refraction will be:

• A. $60^{\circ}$ for both colours
• B. $30^{\circ}$ for both colours
• C. greater for violet colour
• D. greater for red colour

Answer 1

Answer: (B)

As, we know, from Cauchy’s formula, Wavelength $\propto \frac{1}{\mu} $
Since, $\lambda_{voilet} < \lambda_{red} $
Hence from the above equation,
$ \mu_{violet} > \mu_{red} $
For a prism,
$\mu = \frac{sin\,i}{sin \,r} $
As, it is given that angle of incidence is same for both the beams
So, $sin \,r \propto \frac{1}{\mu} $
$ \because \mu_{violet} > \mu_{red} $
$ \therefore sin\, r_{violet } < sin\, r_{red}$
$ \Rightarrow \angle r_{violet} < \angle r_{red}$
Hence, the angle of refraction will be greater for red colour.