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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
Tutti i libri di testoKnight Calc 5th EditionCh 33: Wave OpticsProblema 13
Capitolo 33, Problema 13

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

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Step 1: Recall the diffraction grating equation: d sin(θ) = mλ, where d is the distance between adjacent slits (grating spacing), θ is the diffraction angle, m is the order of the maximum, and λ is the wavelength of light.
Step 2: For the first-order maximum (m = 1), the angle is given as 20.0°. Use this information to determine the ratio λ/d by rearranging the equation: λ/d = sin(20.0°).
Step 3: For the second-order maximum (m = 2), substitute m = 2 and the previously calculated λ/d into the diffraction grating equation: sin(θ_2) = 2(λ/d).
Step 4: Solve for θ_2 by taking the inverse sine: θ_2 = sin-1(2(λ/d)). Use the value of λ/d from Step 2.
Step 5: Verify that the calculated angle θ_2 is physically valid (i.e., sin(θ_2) must be ≤ 1). If sin(θ_2) exceeds 1, the second-order maximum does not exist.

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Diffraction Grating

A diffraction grating is an optical component with a periodic structure that disperses light into its constituent wavelengths. It works on the principle of interference, where light waves overlap and combine, producing distinct patterns of maxima and minima. The spacing between the grating lines determines the angles at which these patterns occur.
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Diffraction

Order of Maximum

The order of maximum refers to the specific bright spots produced in a diffraction pattern, labeled by integers (0, 1, 2, etc.). The first-order maximum is the first bright spot on either side of the central maximum (zeroth order). Each order corresponds to a different angle of diffraction, which can be calculated using the grating equation.
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Grating Equation

The grating equation relates the angle of diffraction to the wavelength of light and the spacing of the grating lines. It is expressed as d sin(θ) = nλ, where d is the distance between grating lines, θ is the angle of the maximum, n is the order of the maximum, and λ is the wavelength. This equation allows for the calculation of angles for different orders of maxima.
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Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen behind the slit. The third maximum is measured to be 3.0 cm from the central maximum. The slits are then illuminated with light of wavelength 440 nm. How far is the fourth maximum from the central maximum?

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In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?

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