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,
$\mu =\frac{sini}{sinr}$
As, it is given that angle of incidence is same for both the beams
So, $sinr\propto \frac{1}{\mu }$
$\because {\mu }_{violet}>{\mu }_{red}$
$\therefore sin{r}_{violet}<sin{r}_{red}$
$\Rightarrow \angle r_{violet}<\angle r_{red}$
Hence, the angle of refraction will be greater for red colour.