---
title: "A monochromatic laser emitting light of wavelength \\(\\lambda\\) is directed at a barrier containing two narrow slits separated by a distance \\(d\\). An interference pattern of bright and dark fringes is observed on a screen located a distance \\(L\\) from the slits. Assume that \\(L\\) is much greater than \\(d\\).   Two students are discussing what would happen to the interference pattern if the original slit barrier is replaced by a new barrier with a smaller slit separation (where \\(d\\) is decreased), while keeping the laser and the screen distance \\(L\\) the same.  **Student 1:** “Because the slits are closer together, the light rays exiting the slits are physically squeezed closer to each other. This means the bright fringes on the screen will also be closer together.”  **Student 2:** “No, the bright fringes only occur where the path length difference between the waves from the two slits is a multiple of the wavelength. If the slits are closer together, the light waves must spread out at a wider angle to achieve that same path length difference, so the bright fringes will be farther apart.”"
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url: "https://nerd-notes.com/ubq/117698/"
date_modified: "2026-08-04T07:53:27+00:00"
---

# A monochromatic laser emitting light of wavelength \(\lambda\) is directed at a barrier containing two narrow slits separated by a distance \(d\). An interference pattern of bright and dark fringes is observed on a screen located a distance \(L\) from the slits. Assume that \(L\) is much greater than \(d\). 

Two students are discussing what would happen to the interference pattern if the original slit barrier is replaced by a new barrier with a smaller slit separation (where \(d\) is decreased), while keeping the laser and the screen distance \(L\) the same.

**Student 1:** “Because the slits are closer together, the light rays exiting the slits are physically squeezed closer to each other. This means the bright fringes on the screen will also be closer together.”

**Student 2:** “No, the bright fringes only occur where the path length difference between the waves from the two slits is a multiple of the wavelength. If the slits are closer together, the light waves must spread out at a wider angle to achieve that same path length difference, so the bright fringes will be farther apart.”

A monochromatic laser emitting light of wavelength \(\lambda\) is directed at a barrier containing two narrow slits separated by a distance \(d\). An interference pattern of bright and dark fringes is observed on a screen located a distance \(L\) from the slits. Assume that \(L\) is much greater than \(d\). 

Two students are discussing what would happen to the interference pattern if the original slit barrier is replaced by a new barrier with a smaller slit separation (where \(d\) is decreased), while keeping the laser and the screen distance \(L\) the same.

**Student 1:** "Because the slits are closer together, the light rays exiting the slits are physically squeezed closer to each other. This means the bright fringes on the screen will also be closer together."

**Student 2:** "No, the bright fringes only occur where the path length difference between the waves from the two slits is a multiple of the wavelength. If the slits are closer together, the light waves must spread out at a wider angle to achieve that same path length difference, so the bright fringes will be farther apart."

![A horizontal laser beam on the left points toward a vertical barrier with two small gaps. A dashed horizontal line passes midway between the two gaps and extends to a vertical rectangular screen on the right. A vertical dimension line between the two gaps is labeled d. A horizontal dimension line between the barrier and the screen is labeled L. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830006-EEYGVj.jpg)

**Part a)** **Evaluate** the claims of both students. **Support your claim** by reasoning using the wave model of light and the concept of path length difference. *(3 points)*

**Part b)** **Derive** an expression for the distance \(\Delta y\) between adjacent bright fringes on the screen. Express your answer in terms of \(d\), \(L\), \(\lambda\), and fundamental constants. Assume the angle \(\theta\) to the fringes is small enough that \(\sin\theta \approx \tan\theta \approx \dfrac{y}{L}\), where \(y\) is the distance from the central maximum. *(3 points)*

**Part c)** **Explain** whether your algebraic derivation in part (b) supports your qualitative reasoning in part (a). *(2 points)*

**Part d)** The original slit barrier with separation \(d\) is placed back into the setup. The original laser is then replaced with a new laser that emits light of a higher frequency. On the axes provided, **sketch** the light intensity versus position \(y\) on the screen for the new laser. The dashed curve represents the interference pattern of the original laser. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117698/*