On the basis of Huygens' wave theory of light prove that velocity of light in a rarer medium is greater than velocity of light in a denser medium.

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Solution

Consider a plane wavefront of monochromatic light obliquely incident at a plane refracting surface $P Q$ separating two mediums. Let $A_{1} B_{1}$ and $A B$ be successive positions of the incident wavefront one wavelength apart and $A_{1} A$ and $B_{1} B$ , the corresponding incident rays. Let $v_{1}$ and $v_{2}$ be the speed of light in medium (1) and medium (2) respectively. If ' $t$ ' is the time taken by the incident ray to cover the distance $B C$ , then $B C = v_{1} t$ . During this time the secondary wavelets originating at $A$ cover a distance $v_{2} t$ in the denser medium. With $A$ as centre draw a hemisphere of radius $v_{2} t$ in the denser medium. It represents the secondary wavefront originating at $A$ . Draw a tangent $C D$ to the secondary wavefront. As all points on $C D$ are in same phase of wave motion, $C D$ represents the refracted wavefront in the denser medium.
So $B C = v_{1} t$
and $A D = v_{2} t$
In $Δ A B C$ $sin i = \frac{B C}{A C}$
In $Δ A C D$ $sin r = \frac{A D}{A C}$
$\frac{sin i}{sin r} = \frac{B C / A C}{A D / A C}$
$= \frac{B C}{A D} = \frac{v_{1} t}{v_{2} t}$
$\frac{sin i}{sin r} = \frac{v_{1}}{v_{2}}$
as $i > r$
So $sin i > sin r$
and because $_{1} μ_{2} > 1$
So $v_{1} > v_{2}$
i.e., velocity of light in a rarer medium is greater than the velocity of light in denser medium.

Suggest Corrections

(a)	Scattering
(b)	Interference
(c)	Diffraction
(d)	Velocity of light in a denser medium is less than the velocity of light in the rarer medium.