Question

Young's experiment is performed with light from excited helium atoms (LaTeX: \lambdaλ=502 nm). Fringes are measured carefully on a screen 1.33 m away from the double slit, and the center of the 18th fringe (not counting the central bright fringe) is found to be 10.7 mm from the center of the central bright fringe. What is the separation of the two slits? Give an answer in mm. Pay attention to the number of significant figures.

Answer 1

Answer:

d = 1.12 mm

Explanation:

The expression for the separation of the interference lines in Young's double slit experiment, for constructive interference is

     d sin θ = m λ

Where d is the separation of the slits, m is the order of interference and λ is the wavelength

Let's use trigonometry to separate the lines on the screen

   tan θ = y/L

As the angles are very small

   tan θ = sin θ / cos θ ≈ Sen θ

We substitute in the initial equation

   d (y/L) = m λ

Let's calculate

    d = m λ L / y

Reduce the SI System

    λ = 502 nm = 502 10⁻⁹ m

    L = 1.33 m

    m = 18

     y = 10.7 mm = 10.7 10⁻³ m

     d = 18 502 10⁻⁹ 1.33 /10.7 10⁻³

    d = 1.12 10⁻³ m

    d = 1.12 mm

We give the answer with three significant figures because all experimental measures have three figures, n is an integer and is not an experimental measure.