Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 34: Problem 16

In a single-slit diffraction pattern, there is a bright central maximum surrounded by successively dimmer higher-order maxima. Farther out from the central maximum, eventually no more maxima are observed. Is this because the remaining maxima are too dim? Or is there an upper limit to the number of maxima that can be observed, no matter how good the observer's eyes, for a given slit and light source?

Short Answer

Expert verified
Answer: There is an upper limit to the number of maxima that can be observed for a given slit and light source in a single-slit diffraction pattern, regardless of the observer's vision. The maxima are not observed beyond a certain point due to the condition for constructive interference, not because of being too dim.

Step by step solution

01

Understand Single-Slit Diffraction Pattern

A single-slit diffraction pattern occurs when light passes through a small slit and interferes in such a way that certain angles create constructive interference (bright fringes or maxima) and other angles create destructive interference (dark fringes). The pattern is characterized by a central maximum and other alternating bright and dark fringes on both sides of this central maximum.
02

Derive the condition for single-slit diffraction maxima

To find the angles at which the maxima occur, we use the condition for constructive interference, which is given by the formula: d sin(θ) = mλ Where d is the width of the slit, θ is the angle formed by the light path with respect to the central maximum, m is the order of the maxima (0, 1, 2, ...), and λ is the wavelength of the light.
03

Determine the range of possible angles and m values

The constructive interference angles, θ, can vary from 0 (which corresponds to the central maximum) up to 90 degrees (which corresponds to the side edge of the screen). Also, the sin(θ) values range between 0 and 1. Additionally, m values must be integers (m=0, 1, 2,...). We can rewrite the condition for maxima as: sin(θ) = mλ / d Now, using the fact that sin(θ) can only vary between 0 and 1: 0 ≤ mλ / d ≤ 1
04

Investigate the limit of m values

From the inequality in step 3, we can find the upper limit for m: mλ / d ≤ 1 ⇒ m ≤ d / λ This inequality indicates that there is indeed an upper limit to the number of maxima that can be observed for a given slit and light source. As m approaches d/λ, the angle θ will approach 90°, meaning that the bright fringes will be close to the edge of the screen, and no further maxima will be observed beyond this point.
05

Conclusion

In a single-slit diffraction pattern, there is an upper limit to the number of maxima that can be observed for a given slit and light source, regardless of the observer's vision. This limit depends on the width of the slit and the wavelength of the light, and the maxima are not observed beyond a certain point due to the condition for constructive interference rather than because of being too dim.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Light from an argon laser strikes a diffraction grating that has 7020 grooves per centimeter. The central and firstorder principal maxima are separated by \(0.332 \mathrm{~m}\) on a wall \(1.00 \mathrm{~m}\) from the grating. Determine the wavelength of the laser light.

White light is shone on a very thin layer of mica \((n=1.57),\) and above the mica layer, interference maxima for two wavelengths (and no other in between) are seen: one blue wavelength of \(480 \mathrm{nm},\) and one yellow wavelength of \(560 \mathrm{nm} .\) What is the thickness of the mica layer?

Light of wavelength \(653 \mathrm{nm}\) illuminates a slit. If the angle between the first dark fringes on either side of the central maximum is \(32.0^{\circ},\) What is the width of the slit?

Many astronomical observatories, and especially radio observatories, are coupling several telescopes together. What are the advantages of this?

A diffraction grating has \(4.00 \cdot 10^{3}\) lines \(/ \mathrm{cm}\) and has white light \((400 .-700 . \mathrm{nm})\) incident on it. What wavelength(s) will be visible at \(45.0^{\circ} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Particle Model of Matter

Read Explanation

Linear Momentum

Read Explanation

Energy Physics

Read Explanation

Electricity

Read Explanation

Radiation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free