Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 32: Problem 18

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?

Short Answer

Expert verified
The light is diffracted at an angle of 9.05 degrees in first order. A fifth order diffraction is not possible with the given parameters.

Step by step solution

01

Compute the Distance between Slits

First, you need to find the distance between the slits (\(d\)). The given information is that there are 3000 lines/cm. However, the wavelength is in nm, so to keep consistent units, convert the distance between slits to metres using the formula \(d = 1/\text{number of lines per metre}\). Hence, convert the given value to lines/m, which gives 3000 lines/cm * 100 cm/m = 300000 lines/m. Therefore, \(d = 1 / 300000 = 3.33 \times 10^{-6}\) m.
02

Solve for First Order Diffraction

Now, you can substitute the known values into the grating equation to solve for \(\theta\) in first order diffraction (\(m = 1\)). So, \(\sin(\theta) = m \cdot \lambda / d = 1 \cdot 520 \times 10^{-9} \, m / 3.33 \times 10^{-6} \, m\). Solving for \(\theta\) gives \(\theta = \text{arcsin}(0.156) = 9.05\) degrees.
03

Solve for Fifth Order Diffraction

Next, calculate \(\theta\) for fifth order diffraction (\(m = 5\)). Substituting these values into the grating equation gives \(\sin(\theta) = m \cdot \lambda / d = 5 \cdot 520 \times 10^{-9}\) m / \(3.33 \times 10^{-6}\) m. Solving for \(\theta\) gives \(\theta = \text{arcsin}(0.780)\). This value is greater than 1, meaning it's not possible to have a fifth order diffraction with these parameters.

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

Why don't you see interference effects between the front and back of your eyeglasses?

Find the intensity as a fraction of the central peak intensity for the second secondary maximum in single-slit diffraction, assuming the peak lies midway between the second and third minima.

Why does an oil slick show colored bands?

A double-slit experiment has slit spacing \(0.12 \mathrm{mm}\). (a) What should be the slit-to-screen distance \(L\) if the bright fringes are to be \(5.0 \mathrm{mm}\) apart when the slits are illuminated with 633 -nm laser light? (b) What will be the fringe spacing with 480 -nm light?

The 546 -nm green line of gaseous mercury falls on a double-slit apparatus. If the fifth dark fringe is at \(0.113^{\circ}\) from the centerline, what's the slit separation?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Radiation

Read Explanation

Physics of Motion

Read Explanation

Solid State Physics

Read Explanation

Electrostatics

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