Question

Two thin parallel slits that are 12.8 LaTeX: \muμm apart are illuminated by a laser beam of wavelength 585 nm. The interference pattern is observed on a very distant large screen. What it the total number of bright fringes (those indicating complete constructive interference), including the central fringe and those on both sides of it?

Answer 1

Answer:

43

Explanation:

Given that distance between two thin parallel slits = 12.8 μm = 12.8 × 10⁻⁶ m

Wavelength (λ) = 585 nm = 585 × 10⁻⁹ m

The angle between bright fringes (θ) is given by:

dsin(θ) = mλ

The farthest brightest fringe is at an angle of 90⁰ from the central bright fringe. At maximum angle θ = 90⁰, m = $m_{max}$. Hence:

$dsin(\theta)=m_{max}\lambda\\\\m_{max}=\frac{dsin(\theta)}{\lambda}\\ \\Substituting:\\\\m_{max}=\frac{12.8*10^{-6}*sin(90^o)}{585*10^{-9}}\\\\m_{max}=21.88\\\\m_{max}\ is\ an\ integer, hence:\\\\m_{max}=21$

Therefore there are 21 bright fringes above the central bright fringe and 21 bright fringe below the central bright fringe and the central bright fringe.

The total number of bright fringes = 21 + 21 + 1 = 43