Question

A student performing a double-slit experiment is using a green laser with a wavelength of $530\mathrm{nm}.$. She is confused when the $m=5$maximum does not appear. She had predicted that this bright fringe would be $1.6\mathrm{cm}$from the central maximum on a screen $1.5\mathrm{m}$behind the slits.

a. Explain what prevented the fifth maximum from being observed.

b. What is the width of her slits?

Short answer

a. The reason is that the $m=5$interference maximum fell exactly on the first minimum in the diffraction pattern which caused a missing order.

b. The width of her slits$a=50\mu \mathrm{m}$

Step-by-step solution

Interference and Diffraction (part a)

a) The reasoning for this is often that pattern on the screen is formed by interference and diffraction from individual single slits, and in some scenarios, an interference maximum occurs with just a diffraction pattern minimum, resulted during a missing order. The interference maximum rested exactly on the primary minimum within the focal plane within the case of the scholar, therefore the predicted sharp fringes during this position isn't seen.

Dark Fringes (part b)

We indicated in portion (a) that the m=5 interference maximum coincides with the first minimum in the diffraction pattern, implying that they are both the same distance from the Centre maximum. As a result, for the diffraction pattern's first dark fringe.

$y_p=\frac{p\lambda L}{a}p=1,2,3,\dots$

$y_1=\frac{\lambda L}{a}$

$a=\frac{\lambda L}{y_1}=\frac{\left(1.5\mathrm{m}\right)\times \left(530\times {10}^{-9}\mathrm{m}\right)}{1.6\times {10}^{-2}\mathrm{m}}=4.97\times {10}^{-5}\mathrm{m}$

$a=50\mu \mathrm{m}$