Physics - Geometrical Optics Question with Solution | TestHub

Angle of incidence, $i=45^{\circ }$

Angle of deviation, $\delta =15^{\circ }$

Since the wave travels from a rarer medium (air) to a denser medium (liquid), it bends towards the normal. The angle of refraction is given by:

$r=i-\delta =45^{\circ }-15^{\circ }=30^{\circ }$

Using Snell's law:

$\frac{\sin i}{\sin r}=\frac{c}{v}$

Substituting the given values:

$\frac{\sin 45^{\circ }}{\sin 30^{\circ }}=\frac{3\times 10^8}{v}$

$\frac{1/\sqrt{2}}{1/2}=\frac{3\times 10^8}{v}$

$\sqrt{2}=\frac{3\times 10^8}{v}$

$v=\frac{3\times 10^8}{\sqrt{2}}=1.5\times \sqrt{2}\times 10^8$

$v\approx 1.5\times 1.414\times 10^8\approx 2.12\times 10^8$ m/s

Answer: $2.1\times 10^8$ m/s