Question

Calculate the refractive index of an equilateral glass prism for a light of red color. The angle of minimum deviation for red color is $30°$.

Answer 1

Step 1: Given data.

The angle of the equilateral prism is $\left(\mathrm{A}\right)\mathrm{is}{60}^{\mathrm{o}}$

Minimum deviation for red color ${\mathrm{D}}_{\min }={30}^{\mathrm{o}}$

Step 2: Find the refractive index $\left(\mathrm{\mu }\right)$.

$\mathrm{Refractive}\mathrm{index}\left(\mathrm{\mu }\right)=\frac{\sin \left({\displaystyle \frac{{\mathrm{D}}_{\min }+\mathrm{A}}{2}}\right)}{\sin \left({\displaystyle \frac{\left(\mathrm{A}\right)}{2}}\right)}$

Putting the values in the formula.

$\mu =\frac{\sin \left({\displaystyle \frac{30+60}{2}}\right)}{\sin \left({\displaystyle \frac{60}{2}}\right)}=\sqrt{2}$

Thus, the refractive index of an equilateral glass prism for a light of red color is $\sqrt{2}$.