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 33

Capitolo 33, Problema 33

Infrared light of wavelength 2.5 μm illuminates a 0.20-mm-diameter hole. What is the angle of the first dark fringe in radians? In degrees?

Guida verificata passo dopo passo

Step 1: Recognize that this is a diffraction problem involving a circular aperture. The angle to the first dark fringe for a circular aperture is given by the formula:

θ = 1.22 \times \frac{λ}{D}

, where

λ

is the wavelength of the light and

D

is the diameter of the aperture.

Step 2: Convert the given values into consistent SI units. The wavelength

λ

is given as 2.5 μm, which is equivalent to

2.5 \times 10 ⁻ 6

meters. The diameter

D

is given as 0.20 mm, which is equivalent to

2.0 \times 10 ⁻ 4

meters.

Step 3: Substitute the values of

λ

and

D

into the formula for

θ

θ = 1.22 \times \frac{2.5 \times 10 ⁻ 6}{2.0 \times 10 ⁻ 4}

. Simplify the fraction to find

θ

in radians.

Step 4: To convert the angle from radians to degrees, use the conversion factor:

1 rad = \frac{180}{π} \deg

. Multiply the angle in radians by this factor to find the angle in degrees.

Step 5: Verify the units and ensure the calculations are consistent. The final answers will be the angle of the first dark fringe in both radians and degrees.

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Concetti chiave

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Diffraction

Diffraction is the bending of waves around obstacles and the spreading of waves when they pass through small openings. In the context of light, diffraction patterns are created when light waves encounter an aperture, leading to regions of constructive and destructive interference. This phenomenon is crucial for understanding how light behaves when it passes through the hole mentioned in the question.

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Percorso guidato

08:44

Diffraction

Single-Slit Diffraction

Single-slit diffraction refers to the pattern of light and dark fringes produced when light passes through a narrow slit or hole. The angle of the dark fringes can be calculated using the formula sin(θ) = mλ/a, where m is the order of the dark fringe, λ is the wavelength of light, and a is the width of the slit. This concept is essential for determining the angle of the first dark fringe in the given problem.

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Percorso guidato

12:33

Single Slit Diffraciton

Wavelength

Wavelength is the distance between successive peaks of a wave, typically measured in meters or micrometers for light. It is a fundamental property of waves that influences their behavior, including diffraction patterns. In this question, the wavelength of the infrared light (2.5 μm) is critical for calculating the angle of the dark fringe, as it directly affects the spacing of the diffraction pattern.

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Percorso guidato

05:42

Unknown Wavelength of Laser through Double Slit

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