Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

34. Wave Optics

Single Slit Diffraction

Physics

34. Wave Optics

Single Slit Diffraction

Previous problemNext problem

4:51 minutes

Problem 67

Textbook Question

Light of wavelength 5.0 x 10⁻⁷ passes through two parallel slits and falls on a screen 5.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart.
(a) Find the distance between the slits.
(b) The same two slits are next illuminated by light of a different wavelength, and the fifth minimum for this light occurs at the same point on the screen as the fourth minimum for the previous light. What is the wavelength of the second source of light?

Verified step by step guidance

Step 1: For part (a), use the formula for the fringe spacing in a double-slit interference pattern: Δy = (λL) / d, where Δy is the fringe spacing (2.0 cm = 0.02 m), λ is the wavelength of the light (5.0 x 10⁻⁷ m), L is the distance to the screen (5.0 m), and d is the distance between the slits. Rearrange the formula to solve for d: d = (λL) / Δy.

Step 2: Substitute the given values into the formula for d: λ = 5.0 x 10⁻⁷ m, L = 5.0 m, and Δy = 0.02 m. Perform the calculation to find the distance between the slits, d.

Step 3: For part (b), recognize that the condition for minima in a double-slit interference pattern is given by the equation: d sin(θ) = mλ, where m is the order of the minimum, λ is the wavelength, and θ is the angle of the minimum. For the first light source, the fourth minimum corresponds to m₁ = 4, and for the second light source, the fifth minimum corresponds to m₂ = 5.

Step 4: Since the fifth minimum of the second light source coincides with the fourth minimum of the first light source, the path difference for both cases must be the same. Set up the equality: m₁λ₁ = m₂λ₂, where λ₁ is the wavelength of the first light (5.0 x 10⁻⁷ m) and λ₂ is the wavelength of the second light. Rearrange the equation to solve for λ₂: λ₂ = (m₁λ₁) / m₂.

Step 5: Substitute the known values into the equation for λ₂: m₁ = 4, λ₁ = 5.0 x 10⁻⁷ m, and m₂ = 5. Perform the calculation to find the wavelength of the second source of light, λ₂.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Young's Double Slit Experiment

Young's Double Slit Experiment demonstrates the wave nature of light through the interference pattern created when light passes through two closely spaced slits. The pattern consists of alternating bright and dark bands on a screen, resulting from constructive and destructive interference of light waves. The distance between the slits, the wavelength of the light, and the distance to the screen are crucial for calculating the positions of these bands.

Interference Pattern

An interference pattern is formed when two or more coherent light waves overlap, leading to regions of constructive interference (bright bands) and destructive interference (dark bands). The spacing of these bands is influenced by the wavelength of the light and the geometry of the slits. The distance between adjacent bright or dark bands can be used to derive important parameters such as slit separation and wavelength.

Wavelength and Minima

The wavelength of light is the distance between successive peaks of a wave, and it plays a critical role in determining the positions of minima in an interference pattern. For a double slit setup, the positions of the minima can be calculated using the formula for destructive interference, which involves the wavelength and the slit separation. When comparing two different wavelengths, the relationship between their respective minima can help determine unknown wavelengths based on their positions on the screen.

Watch next

Master Single Slit Diffraciton with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

Explain why the secondary maxima in the single-slit diffraction pattern do not occur precisely at β/2 = (m + 1/2)π where m = 1, 2, 3, ... Carefully and precisely plot the curves y = β/2 and y = tan β/2. From their intersections, determine the values of β for the first and second secondary maxima. What is the percent difference from β/2 = (m + 1/2)π?

views

Textbook Question

A 20x telescope has a 12-cm-diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?

views

Textbook Question

(II) A lens appears greenish yellow (λ = 570nm is strongest) when white light reflects from it. What minimum thickness of coating (n = 1.25) do you think is used on such a glass lens (n = 1.56), and why?

views

Textbook Question

A thin oil slick (n_o = 1.50) floats on water (n_w = 1.33). When a beam of white light strikes this film at normal incidence from air, the only enhanced reflected colors are red (653 nm) and violet (392 nm). From this information, deduce the (minimum) thickness t of the oil slick.

views

Textbook Question

A highly reflective mirror can be made for a particular wavelength at normal incidence by using two thin layers of transparent materials of indices of refraction n₁ and n₂ ( 1 < n₁ < n₂ ) on the surface of the glass (n > n₂). What should be the minimum thicknesses d₁ and d₂ in Fig. 34–49 in terms of the incident wavelength λ, to maximize reflection?

views

Multiple Choice

Light from a 600 nm laser is shown through a single slit of unknown width. If a screen is placed 4.5 m behind the slit captures a diffraction patter with a central bright fringe of width 20 mm, what is the width of the single slit?

A single slit is illuminated by coherent monochromatic light at