Question

The line-width of a bright fringe is sometimes defined as the separation between the points on the two sides of the central line where the intensity falls to half the maximum. Find the line-width of a bright fringe in a Young's double slit experiment in terms of λ, d and D where the symbols have their usual meanings.

Answer 1

Explanation:

i) When intensity is half the maximum l/l base max = 1/2 ⇒ 4a^2 cos^2(∅/2)/4a^2 = 1/4 ⇒ cos^2 (∅/2) = 1/4 ⇒ cos(∅/2) = 1/2 ⇒ ∅/2 = π/3 ⇒ ∅ = 2π/3 ⇒ Path difference, * = λ/3 ⇒ y = xD/d = λD/3d

Answer 2

The line-width of a bright fringe in a Young's double slit experiment in terms of λ, d and D where the symbols have their usual meanings is $\frac{\lambda \mathbf{D}}{2 d}$

Explanation:

• Often, the line width of a bright fringe is known as the distance Between the points at the center line on both sides where the level decreases to half the mark. We know that, to a maximum of half the level  

• Line-width of a light fringe in the double-slit experiment at Young λ, d and D Such symbols have their normal significances.

$y=\pm \frac{\lambda \mathrm{D}}{4 d}$

Line width $=\frac{\lambda \mathbf{D}}{4 d}+\frac{\lambda \mathbf{D}}{4 d}$

Line width  $=\frac{\lambda D+\lambda D}{4 d}$

Line width  $=\frac{2 \lambda D}{4 d}$

Line width  $=\frac{\lambda \mathbf{D}}{2 d}$