Question

A ray of light is incident on one face of prism with refracting angle $A(<{90}^{\circ })$. The incident ray is normal to the other face of the prism. If C is the critical angle for prism air interface, then the ray will emerge from this faces only if

• A. $cotC<cotA+1$
• B. $cotC>cotA+1$
• C. $cotA<cotC+1$
• D. $cotA>cotC+1$

Answer 1

The correct option is A $cotC<cotA+1$

A ray of light is incident on one face of prism with refracting angle A $\left(\angle {90}^o\right)$ .

The incident ray is normal to each other face of the prism

(Refer to Image)

$\frac{\sin C}{\cos C}=\frac{\frac{1}{\cos C}}{\sin C}=\cot C$

and $\frac{\sin A}{\sin B}=\cot A+1$ .