Question

a) Describe Young's experiment in interference with necessary theory.
b) Mention the shape of wave front for the portion of wave front of light from a distant star intercepted by the earth.

Answer 1

Double slit experiment

The phenomenon of interference was first observed and demonstrated by Thomas Young in 1801. The experimental set up is shown in figure.

In double slit experiment, we use two long parallel slits as the source of light. The light coming out of the two slits is intercepted on a screen placed parallel to the plane of the slits. The slits are illuminated by a parallel beam of a monochromatic light. A series of dark and bright strips, called fringes, are observed on the screen.

Let d be the distance between two coherent sources A and B of wavelength λ. A screen XY is placed parallel to AB at a distance D from the coherent sources. C is the midpoint of AB. O is a point on the screen equidistant from A and B. P is a point at a distance x from O, as shown in the figure. Waves from A and B meet at P in phase or out of phase depending upon the path difference between two waves

Draw AM perpendicular to BP

The path difference $\Delta$X = BP – AP

AP = MP

Interference Band Width

$\Delta$X = BP – AP = BP – MP = BM

In right angled $△$ ABM, BM = d sin θ If θ is small,

sin θ = θ

The path difference $\Delta$X = θ.d

In right angled triangle COP, tan θ = OP/CO = x/D

For small values of θ, tan θ = θ

Thus, the path difference $\Delta$X = xd/D

For bright fringes,

$\Delta$X = n$\lambda$

For dark fringes,

$\Delta$X = (n+1/2)$\lambda$