Question

The width of a plane incident wavefront is found to be doubled in a denser medium. If it makes an angle of ${70}^0$ with the surface, calculate the refractive index for the denser medium.

Answer 1

The width of the plane wave front is doubled and it can be written as,

$\frac{\cos r}{\cos i}=2$

$\frac{\cos r}{\cos {70}^{\circ }}=2$

$r={46.84}^{\circ }$

The refractive index is given as,

$\mu =\frac{\sin i}{\sin r}$

$\mu =\frac{\sin {70}^{\circ }}{\sin {46.84}^{\circ }}$

$\mu =1.288$

Thus, the refractive index in for the denser medium is $1.288$.