Problem 14-10 Double Slit - Part 2 - C

A laser beam with light of wavelength \(638.2\; nm\) is used to check a manufacturer's claim that a double slit has a separation of \(0.200\; mm.\) The distance to the screen is \(3.00\; m\) and the measured distance from the central maximum to the middle of the fourth minimum is \(33.2 \;mm.\) What is the measured slit separation?
[Ans. \(0.202 \;mm\)]

Accumulated Solution
Diagram of laser beam.

\(N = 4 \\ \lambda = 638.2 \times 10^{-9}\; m \\ x = 33.2\times 10^{-3} \; m \\ L = 3.00 \;m\)

Correct!

Solving for \(d\) gives:

\(d = \frac{(N-1/2)\lambda L}{x}= \frac{(4-1/2)(638.2 \times 10^{-9})(3.00)}{33.2 \times 10^{-3}} \\ = 202 \times 10^{-4} \; m = 0.202 \; mm\)

 

You have completed this problem.