Question

The maximum value of index of refraction of a material of a prism which allows the passage of light through it when the refracting angle of the prism is A is

• A. $\sqrt{1+sin\left(\frac{A}{2}\right)}$
  
• B. $\sqrt{1+cos\left(\frac{A}{2}\right)}$
  
• C. $\sqrt{1+ta{n}^2\left(\frac{A}{2}\right)}$
  
• D. $\sqrt{1+co{t}^2\left(\frac{A}{2}\right)}$

Answer 1

The correct option is D $\sqrt{1+co{t}^2\left(\frac{A}{2}\right)}$

Situation is shown in figure.

$r_1=C,r_2=C{r}_1+r_2=A\therefore 2C=A,C=\frac{A}{2}\therefore \mu =\frac{1}{sinC}=\frac{1}{sin\left(\frac{A}{2}\right)}=\frac{\sqrt{si{n}^2\left(\frac{A}{2}\right)+co{s}^2\left(\frac{A}{2}\right)}}{sin\left(\frac{A}{2}\right)}=\sqrt{1+co{t}^2\left(\frac{A}{2}\right)}$