Ch 33: Wave Optics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 33: Wave Optics

Problema 17

Capitolo 33, Problema 17

FIGURE EX33.17 shows the interference pattern on a screen 1.0 m behind an 800 lines/mm diffraction grating. What is the wavelength (in nm) of the light?

Guida verificata passo dopo passo

Step 1: Understand the problem. The diffraction grating has 800 lines per millimeter, and the screen is located 1.0 m behind the grating. The goal is to calculate the wavelength of the light in nanometers (nm). The diffraction grating equation is used:

d sin θ = m λ

, where d is the spacing between the lines, θ is the diffraction angle, m is the order of the maximum, and λ is the wavelength.

Step 2: Calculate the grating spacing (d). The grating has 800 lines per millimeter, so the spacing between the lines is the reciprocal of the number of lines per unit length. Convert millimeters to meters:

d = \(\frac{1}{800 \times 10^3}\)

meters.

Step 3: Identify the diffraction order (m) and the angle (θ) from the interference pattern shown in the figure. The angle θ can be determined geometrically using the position of the bright fringe on the screen and the distance to the screen. Use trigonometry:

\(\tan\) θ = \(\frac{y}{L}\)

, where y is the distance of the fringe from the central maximum and L is the distance to the screen.

Step 4: Rearrange the diffraction grating equation to solve for the wavelength (λ):

λ = \(\frac{d \sin θ}{m}\)

. Substitute the values for d, θ, and m into the equation.

Step 5: Convert the wavelength from meters to nanometers. Since 1 nanometer (nm) is equal to

10^{-9}

meters, multiply the result by

10^9

to express the wavelength in nanometers.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Diffraction Grating

A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams. The spacing between the lines on the grating determines the angles at which light of different wavelengths will constructively interfere, creating an interference pattern. In this case, the grating has 800 lines per millimeter, which is crucial for calculating the wavelength of the light.

Video consigliato:

Percorso guidato

08:44

Diffraction

Interference Pattern

An interference pattern is a series of light and dark bands created when waves overlap and combine. Constructive interference occurs when waves are in phase, leading to bright spots, while destructive interference occurs when waves are out of phase, resulting in dark spots. The pattern observed on the screen is a direct result of the light waves interacting after passing through the diffraction grating.

Video consigliato:

Percorso guidato

03:47

Wave Interference & Superposition

Wavelength Calculation

The wavelength of light can be determined using the formula for diffraction, which relates the angle of the interference pattern to the wavelength, the distance to the screen, and the grating spacing. The formula is given by d sin(θ) = mλ, where d is the distance between grating lines, θ is the angle of the m-th order maximum, and λ is the wavelength. This relationship allows for the calculation of the wavelength based on the observed interference pattern.

Video consigliato:

Percorso guidato

05:42

Unknown Wavelength of Laser through Double Slit

Pratica correlata

Domanda del libro di testo

A diffraction grating produces a first-order maximum at an angle of 20.0°. What is the angle of the second-order maximum?

192

views

Domanda del libro di testo

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm, and the light is observed on a screen 1.50 m behind the grating. What is the distance between the first-order red and blue fringes?

114

views

Domanda del libro di testo

In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width (in mm) of the central maximum on a screen 2.0 m behind the slit?

173

views

Domanda del libro di testo

Light of 630 nm wavelength illuminates a single slit of width 0.15 mm. FIGURE EX33.22 shows the intensity pattern seen on a screen behind the slit. What is the distance to the screen?

201

views

Domanda del libro di testo

A double-slit interference pattern is created by two narrow slits spaced 0.25 mm apart. The distance between the first and the fifth minimum on a screen 60 cm behind the slits is 5.5 mm. What is the wavelength (in nm) of the light used in this experiment?

1817

views

Domanda del libro di testo

Light of 600 nm wavelength passes through a single slit and creates a 2.0-cm-wide central maximum on a screen behind the slit. What wavelength of light will create a 3.0-cm-wide central maximum on a screen twice as far away?

119

views