Question

a) Define a wave front. 

b) Draw the diagram to show the shape of plane wave front as they pass through (i) a thin prism and (ii) a thin convex lens. State the nature of refracted wave front. 

c) Verify Snell’s law of refraction using Huygens’s principle.

Answer 1

(a) Wave Front:  In a wave emanating from the source, locus of a point which oscillate in phase is called a wave front.

(b) Refraction of a plane wave by 

(i) A thin prism:

(ii) A thin Convex lens

(c) Snell's law of refraction using Huygens Principle 

A plane wave AB is incident at an angle i on the surface pp' since v₂ < v₁, the refracted waves bends towards the normal.

Let t be the time taken by the wave front AB to travel the distance BC.

\(\therefore\) BC = v₁t

Also, AE = v₂t

Now, In \(\triangle\)ABC and \(\triangle\)AEC,

sin i = \(\frac{BC}{AC}\) = \(\frac{v_1t}{AC}\)

sin r = \(\frac{AE}{AC}\) = \(\frac{v_2t}{AC}\)

\(\therefore\) \(\frac{\sin\,i}{\sin\,r}\) = \(\frac{v_1}{v_2}\)

Also, absolute refractive index of medium 1, n₁ = \(\frac{c}{v_1}\) \(\Rightarrow\) v₁ = \(\frac{c}{n_1}\)

similarly,n₂ = \(\frac{c}{v_2}\)\(\Rightarrow\)  v₂ = \(\frac{c}{n_2}\)

\(\therefore\) \(\frac{\sin\,i}{\sin\,r}\) = \(\frac{\frac{c}{n_1}}{\frac{c}{n_2}}\) = \(\frac{n_2}{n_1}\)

Or,

n1sin i = n2 sin r

This is Snell's law of refraction.

Answer 2

(a) Definition of wavefront 

(b) Ray diagram showing shapes of wavefront

(c) Proof of Snell’s law