Physics - Geometrical Optics Question with Solution | TestHub

By Snell's law, we have $\sin i=\mu \sin r$, which gives $\frac{1}{\mu }=\frac{\sin r}{\sin i}$.

The angle of deviation is $\delta =i-r$, which implies $r=i-\delta$.

Substituting this into the expression for $\frac{1}{\mu }$:

$\frac{1}{\mu }=\frac{\sin (i-\delta )}{\sin i}$

Expanding the numerator using the identity $\sin (A-B)=\sin A\cos B-\cos A\sin B$:

$\frac{1}{\mu }=\frac{\sin i\cos \delta -\cos i\sin \delta }{\sin i}$

Dividing each term by $\sin i$:

$\frac{1}{\mu }=\cos \delta -\cot i\sin \delta$

$\frac{1}{\mu }=\cos \delta -\frac{\sin \delta }{\tan i}$

Answer: $\frac{1}{\mu }=\cos \delta -\frac{\sin \delta }{\tan i}$