Question

$AB$ and $CD$ are two slabs. The medium between the slabs has refractive index as shown in the figure. Minimum angle of incidence (in degrees) at $Q$ , so that the ray is totally reflected by both the slabs is

a

• A. $60$
• B. $30$
• C. $45$
• D. $15$

Answer 1

Answer: (A)

Critical angles at 1 and 2

${\theta }_{c_1}={\sin }^{-1}\left(\frac{{\mu }_1}{{\mu }_2}\right)={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)=45^0$
${\theta }_{c_2}={\sin }^{-1}\left(\frac{{\mu }_3}{{\mu }_2}\right)={\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^0$
Therefore, minimum angle of incidence for total internal reflection to take place on both slabs should be 60⁰