Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 53

For 600-nm wavelength light and a slit separation of \(0.12 \mathrm{mm},\) what are the angular positions of the first and third maxima in the double slit interference pattern?

Short Answer

Expert verified
The angular positions of the first and third maxima in the double-slit interference pattern for a 600-nm wavelength light and a slit separation of $0.12\,\text{mm}$ are approximately \(0.288^\circ\) and \(0.858^\circ\), respectively.

Step by step solution

01

Convert units

We first need to make sure that the units are consistent before plugging the values into the formula. The given wavelength is in nm and the slit separation is in mm. It is easier to convert nm to mm in this case. Remember that 1 nm = \(10^{-6}\) mm. Thus, \(600\,\text{nm} = 600 \times 10^{-6}\, \text{mm} = 6.0 \times 10^{-4}\, \text{mm} \)
02

Find the angular position of the first maximum \(m = 1\)

Now, we can use the formula \(\sin \theta = \frac{m\lambda}{d}\) to find the angular position for the first maximum, which corresponds to \(m = 1\). So, \( \sin \theta_1 = \frac{1 \times 6.0 \times 10^{-4}\,\text{mm}}{0.12\, \text{mm}} \) Calculate the angle \(\theta_1\): \( \theta_1 = \arcsin\left(\frac{6.0 \times 10^{-4}\,\text{mm}}{0.12\, \text{mm}}\right) \)
03

Find the angular position of the third maximum \(m = 3\)

Next, we need to find the angular position for the third maximum (where \(m = 3\)). Use the same formula, but replace the value of \(m\) with 3: \( \sin \theta_3 = \frac{3 \times 6.0 \times 10^{-4}\,\text{mm}}{0.12\, \text{mm}} \) Calculate the angle \(\theta_3\): \( \theta_3 = \arcsin\left(\frac{3 \times 6.0 \times 10^{-4}\,\text{mm}}{0.12\, \text{mm}}\right) \)
04

Calculate the angles and present the answer in degrees

Now, we can compute the angles \(\theta_1\) and \(\theta_3\) using a calculator: \( \theta_1 \approx 0.00503\,\text{rad} \approx 0.288^\circ \\ \theta_3 \approx 0.01497\,\text{rad} \approx 0.858^\circ \) Thus, the angular positions of the first and third maxima are approximately \(0.288^\circ\) and \(0.858^\circ\), respectively.

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

Describe how a Michelson interferometer can be used to measure the index of refraction of a gas (including air).

A good quality camera "lens" is actually a system of lenses, rather than a single lens, but a side effect is that a reflection from the surface of one lens can bounce around many times within the system, creating artifacts in the photograph. To counteract this problem, one of the lenses in such a system is coated with a thin layer of material \((n=1.28)\) on one side. The index of refraction of the lens glass is \(1.68 .\) What is the smallest thickness of the coating that reduces the reflection at \(640 \mathrm{nm}\) by destructive interference? (In other words, the coating's effect is to be optimized for \(\lambda=640 \mathrm{nm} .)\)

What is the wavelength of light falling on double slits separated by \(2.00 \mu \mathrm{m}\) if the third-order maximum is at an angle of \(60.0^{\circ} ?\)

Is it possible to create a experimental setup in which there is only destructive interference? Explain.

A Michelson interferometer with a He-Ne laser light source \((\lambda=632.8 \mathrm{nm})\) projects its interference pattern on a screen. If the movable mirror is caused to move by \(8.54 \mu \mathrm{m},\) how many fringes will be observed shifting through a reference point on a screen?
See all solutions

Recommended explanations on Physics Textbooks

Modern Physics

Read Explanation

Medical Physics

Read Explanation

Oscillations

Read Explanation

Electricity and Magnetism

Read Explanation

Wave Optics

Read Explanation

Magnetism

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