Name: Brewster’s Law
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: Light is a transverse electromagnetic wave with electric field vectors vibrating in infinite directions perpendicular to the direction of propagation. Let's...

Question

Explain Young&rsquo;s double slit experiment to produce interference pattern due to monochromatic source of light. Deduce an expression for fringe-width.

Accepted Answer

Young’s Double slit experiment: Coherent sources are those which have exactly the same frequency and are in this same phase or have a constant difference in phase.

Conditions: (i) The sources should be monochromatic and originating from common single source. (ii) The amplitudes of the waves should be equal.

Fringe Width β: The distance between any two consecutive bright fringes or any two consecutive dark fringes is called the fringe width. It is denoted by $ω$ ..

For Bright Fringes: If $y_{n + 1}$ and $y_{n}$ denote the distances of two consecutive bright fringes from $M$ , then we have

$y_{n + 1} = (n + 1) \frac{D λ}{d} a n d y_{n} = \frac{n D λ}{d}$

$∴$ Fringe width, $β = y_{n + 1} - y_{n} = (n + 1) \frac{D λ}{d} - \frac{n D λ}{d} = \frac{D λ}{d} .$

For dark fringes-If $y_{n + 1}$ and $y_{n}$ are the distance of two consecutive dark fringes from $M$ ,then we have

$∴$ Fringe width $β = y_{n + 1} - y_{n} = (n + \frac{1}{2}) \frac{D λ}{d} - (n - \frac{1}{2}) \frac{D λ}{d} = \frac{D λ}{d} (n + \frac{1}{2} - n + \frac{1}{2}) = \frac{D λ}{d} .$

Explain Young’s double slit experiment to produce interference pattern due to monochromatic source of light. Deduce an expression for fringe-width.

Important Questions on Wave Optics

Learn and Prepare for any exam you want !