Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 25: Problem 53

A beam of yellow laser light \((590 \mathrm{nm})\) passes through a circular aperture of diameter \(7.0 \mathrm{mm}\). What is the angular width of the central diffraction maximum formed on a screen?

Short Answer

Expert verified
Question: Calculate the angular width of the central diffraction maximum formed on a screen when a light beam with a wavelength of \(590\) nm passes through a circular aperture with a diameter of \(7.0\) mm. Answer: The angular width of the central diffraction maximum is approximately \(5.85 \times 10^{-3}\) degrees.

Step by step solution

01

Identify the given values

Wavelength of the light (\(\lambda\)) = \(590\) nm = \(590 \times 10^{-9}\) m (as we should convert the unit to meters) Diameter of the aperture (\(D\)) = \(7.0\) mm = \(7.0 \times 10^{-3}\) m (as we should convert the unit to meters)
02

Calculate the angular width of the central maximum

Using the formula, \(\theta = 1.22\frac{\lambda}{D}\), we can plug in the given values: \(\theta = 1.22 \frac{(590 \times 10^{-9} \mathrm{m})}{(7.0 \times 10^{-3} \mathrm{m})}\)
03

Solve for the angular width

Calculating the value, we get: \(\theta = 1.22 \frac{(590 \times 10^{-9})}{(7.0 \times 10^{-3})} = 1.02 \times 10^{-4} \mathrm{radians}\) Since the answer should be in degrees, we'll convert radians to degrees: \(\theta = 1.02 \times 10^{-4} \cdot \frac{180}{\pi} \approx 5.85 \times 10^{-3} \mathrm{degrees}\)
04

Write the final answer

The angular width of the central diffraction maximum formed on the screen is approximately \(5.85 \times 10^{-3}\) degrees.

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

Show that the interference fringes in a double-slit experiment are equally spaced on a distant screen near the center of the interference pattern. [Hint: Use the small angle approximation for \(\boldsymbol{\theta} .]\)
The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of \(305 \mathrm{m}(1000 \mathrm{ft})\) diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of \(300 \mathrm{MHz}\), what is the angle between two stars that can barely be resolved? (Tutorial:radio telescope).
Parallel light of wavelength \(\lambda\) strikes a slit of width \(a\) at normal incidence. The light is viewed on a screen that is \(1.0 \mathrm{m}\) past the slits. In each case that follows, sketch the intensity on the screen as a function of \(x\), the distance from the center of the screen, for $0 \leq x \leq 10 \mathrm{cm}$ (a) \(\lambda=10 a\). (b) \(10 \lambda=a,\) (c) \(30 \lambda=a.\)
When Albert turns on his small desk lamp, the light falling on his book has intensity \(I_{0} .\) When this is not quite enough, he turns the small lamp off and turns on a high-intensity lamp so that the light on his book has intensity \(4 I_{0} .\) What is the intensity of light falling on the book when Albert turns both lamps on? If there is more than one possibility, give the range of intensity possibilities.
A Michelson interferometer is set up using white light. The arms are adjusted so that a bright white spot appears on the screen (constructive interference for all wavelengths). A slab of glass \((n=1.46)\) is inserted into one of the arms. To return to the white spot, the mirror in the other arm is moved $6.73 \mathrm{cm} .$ (a) Is the mirror moved in or out? Explain. (b) What is the thickness of the slab of glass?
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Nuclear Physics

Read Explanation

Famous Physicists

Read Explanation

Thermodynamics

Read Explanation

Rotational Dynamics

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