Question

The critical angle for refraction from medium -1 to air is ${\theta }_1$ and that from medium -2 to air is ${\theta }_2$. If medium -2 is denser then medium -1. Find the critical angle for refraction from medium -2 to medium.

• A. ${sin}^{-1}\left(\frac{{sin\theta }_2}{{sin\theta }_1}\right)$
• B. ${sin}^{-1}\left(\frac{{sin\theta }_1}{{sin\theta }_2}\right)$
• C. Both A and B
• D. None of these

Answer 1

The correct option is B ${sin}^{-1}\left(\frac{{sin\theta }_1}{{sin\theta }_2}\right)$

From medium 1 to air

${\eta }_{1}sin{\theta }_1={\eta }_{2}sin{\theta }_2$

here ${\eta }_2$ = 1 (air)

${\eta }_1=\frac{1}{sin{\theta }_1}$

Similarly for medium 2 to air

${\eta }_2=\frac{1}{sin{\theta }_2}$

Now from medium (2) to (1)

${\eta }_{2}sin{\theta }_2={\eta }_{1}sin{\theta }_2$

$sin{\theta }_c=\frac{sin{\theta }_2}{sin{\theta }_1}$

${\theta }_c=si{n}^{-1}\left(\frac{sin{\theta }_2}{sin{\theta }_1}\right)$