Question

Thomas young successfully conducted double-slit experiment and explained the interference phenomenon using Huygens principle. 

1. State Huygens wave theory.

2. State Huygens principle arrive at Snell’s law of refraction.

3. In the word of Hyugens “Light propagates as longitudinal waves” comment on the above statement.

Answer 1

1. According to Huygen’s principle

• Every point in a wavefront act as a source of secondary wavelets.
• The secondary wavelets travel with the same velocity as the original value.
• The envelope of all these secondary wavelets gives a new wavefront.

2. Huygen’s principle: 

According to Huygen’s principle:

• Every point in a wavefront acts as a source of secondary wavelets.
• The secondary wavelets travel with the same velocity as the original value.
• The envelope of all these secondary wavelets gives a new wavefront.

Refraction of a plane wave. (To prove Snell’s law): 

AB is the incident wavefront and c₁ is the velocity of the wavefront in the first medium. CD is the refracted wavefront and c₂ is the velocity of the wavefront in the second medium. AC is a plane separating the two media.

The time taken for the ray to travel from Pto R is

O is an arbitrary point. Hence AO is a variable. But the time to travel a wavefront from AB to CD is constant. In order to satisfy this condition, the term containing AO in eq. (2) should be zero.

∴ \(AO\Big(\frac{sin\,i}{C_1}-\frac{sin\,r}{C_2}\Big)\) = 0

\(\frac{sin\,i}{C_1}=\frac{sin\,r}{C_2}\)

\(\frac{sin\,i}{sin\,r}=\frac{C_1}{C_2}\) = ¹n₂(constant)

where ¹n₂ is the refractive index of the second medium w.r.t. the first. This is the law of refraction.

3. Light wave cannot be longitudinal as it exhibit polarisation.