Question

Figure-$6.112 $shows plane waves refracted from air to water using Huygen's principle $a, b, c, d, e$ are lengths on the diagram. The refractive index of water w.r.t air is the ratio:

• A. a/e
• B. b/e
• C. $b / d$
• D. $d / b$

Answer 1

Answer: (C)

For a wavefront, we know that time taken by all points on it from one position to another of same wavefront are equal. If $t$ is the time taken by the wavefront in travelling from position $AB$ to position $MN$ as shown in figure, then we use
$t v_{m}=d$
$t v_{\text {air }}=b$
Where $v_{m}$ is the speed of light in water and $v_{\text {air }}$ is the speed of light in air.
Dividing the above two equations, we get
$\frac{V_{m}}{V_{a i r}}=\frac{d}{b} $
$\frac{\mu_{m}}{\mu_{a i r}}=\frac{b}{d}$