Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 32: Problem 65

A thin-walled glass tube of length \(L\) containing a gas of unknown refractive index is placed in one arm of a Michelson interferometer using light of wavelength \(\lambda\). The tube is then evacuated. During the process, \(m\) bright fringes pass a fixed point in the viewer. Find an expression for the refractive index of the gas.

Short Answer

Expert verified
The refractive index of the gas in the tube is given by the expression \( n = m \lambda / L + 1 \).

Step by step solution

01

Understand the fundamentals

A Michelson interferometer uses the principle of interference and divides a light beam into two paths and then recombines them to form an interference pattern. The change in the optical path when the tube is evacuated is given by the formula: \( \Delta L = L (n - 1) \), where \( n \) is the refractive index, \(L\) is the length of tube and \( \Delta L \) is the change in optical path length. The movement of \( m \) fringes indicates this change in optical path length, which is equal to \( m \) wavelengths of light.
02

Use the principle of Michelson interferometer

The number of wavelengths in the optical path is the ratio of the optical path length to the wavelength of the light. Therefore, when the tube is evacuated, the number of wavelengths reduces by \( m \). Therefore, \( m = \Delta L / \lambda \) where \( \lambda \) is the wavelength of light.
03

Find the expression for refractive index

Substitute the formula of \( \Delta L \) from step 1 into the equation from step 2 gives \( m = L(n-1) / \lambda \). Rearranging this equation gives us the expression for the refractive index of the gas as \( n = m \lambda / L + 1 \).

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

Green light at \(520 \mathrm{nm}\) is diffracted by a grating with 3000 lines/cm. Through what angle is the light diffracted in (a) first and (b) fifth order?

When the Moon passes in front of a star, the starlight intensity fluctuates before going to zero instead of dropping abruptly. Explain.

A five-slit system with \(7.5-\mu \mathrm{m}\) slit spacing is illuminated with 633 -nm light. Find the angular positions of (a) the first two maxima and (b) the third and sixth minima.

Light with wavelength \(633 \mathrm{nm}\) is incident on a \(2.5-\mu \mathrm{m}\) -wide slit. Find the angular width of the central peak in the diffraction pattern, taken as the angular separation between the first minima.

One arm of a Michelson interferometer is \(42.5 \mathrm{cm}\) long and is enclosed in a box that can be evacuated. The box initially contains air, which is gradually pumped out. In the process, 388 bright fringes pass a point in the viewer. If the interferometer uses light with wavelength \(641.6 \mathrm{nm},\) what's the air's refractive index?
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Translational Dynamics

Read Explanation

Electricity and Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Solid State Physics

Read Explanation

Turning Points in Physics

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