Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

A thin air wedge is formed by introducing a very thin wire of diameter 0.06 mm at one end between the two glass plates, & placed at a distance 0.15 m from the edge. Find the fringe width if $\lambda = 6000 \mathring{A}$.

Diameter d= 0.06 x10$^{-3}$m, length l = 0.15 m, Fringe width, D$_x$ =?, λ= 6000x10$^{-10}$ m

$tan \ ѳ = \frac{d}{l}$…………………….(1)

Also, $ tan \ ѳ = \frac{λ}{2μD_x}$…………….(2)

from 1 & 2 and also refractive index for air is 1

$ \frac{d}{l} = \frac{λ}{2μD_x} \ \ i.e. \ \ d = \frac{lλ}{2D_x} \\[2ex] D_x = \frac{lλ}{2d} \\[2ex] D_x = \frac{0.15 \times 6000 \times10^{-10}}{2 \times 0.06 \times10^{-3}} \\[2ex] D_x = 0.75 \ mm $