physics2 week 6.2 part 1

Chapter 1: Introduction

• Discussion of light waves and their behavior in reaching a screen.

  • Light waves must arrive at a good angle to maintain visibility on the screen.

  • Importance of experimenting to derive laws:

  • Identify relationships through observation.

  • Conduct multiple experiments to understand variability of relationships.

• Introduced terms defining monochromatic light:

  • "Monochromatic":

  • "Mono" means one.

  • "Chromatic" means color.

  • Explanation of the relationship between slit distance and fringe order.

Chapter 2: A Small Angle

• Counting fringe orders from the central plane:

  • Counting up is positive (e.g., +1, +2).

  • Counting down is negative (e.g., -1, -2).

  • Example value given: approximately zero point zero zero three (0.003).

• Suggestion for simplifying angle representation:

  • For small angles, one can represent the angle as ( \theta ) in radians.

  • Important note for exams:

  • If a value is already in radians, fewer details are necessary in calculations.

• Relationship to the equation involving slit distance (d) and fringe positioning.

Chapter 3: Light Because Light

• Personal anecdote about transitioning from fear of the dark to curiosity about light mechanics.

• Introduction of the double slit experiment by Thomas Young:

  • Concept: Utilize two thin slits to observe unexpected patterns (fringes).

• Experiment results:

  • Consistent observations from multiple experiments reinforced initial findings.

  • Query posed: Is it possible to achieve fringes with a single slit?

  • Answer: No, fringes require interference from two waves.

• Explanation of interference:

  • Constructive interference:

  • When waves combine to increase amplitude.

  • Destructive interference:

  • When waves cancel each other out, reducing or eliminating visibility.

Chapter 4: Double Slit Experiment

• Explanation of interference patterns observed in double slit setups.

  • Constructive and destructive interference results in observable fringes on a screen.

• Concept introduction: Cancellation of waves leads to absence of light/impact in certain areas.

• Notable visual concepts when wave fronts are observed:

  • Parallel rings observed during entry, changing direction.

• Assignment emphasis on wave optics with different experiments (e.g., double and single slits).

Chapter 5: The Bright Fringes

• Observation on the appearance of fringes on the screen:

  • The central fringe is larger than others.

  • Overall, bright fringes maintain similar width.

• Suggestion on how to illustrate fringe effects:

  • Use of dotted lines for clarity in representation.

• Note: There’s a differentiation in terminology regarding slits (double vs. single).

Chapter 6: Single Slit Experiment

• Distinction made between double slit and single slit experiments:

  • Single slit involves just one slit focusing on different mechanisms.

• Questions posed about effect of slit width on observed results.

• Introduction to formula adjustments:

  • Replacement of variables (e.g., ( v ) with ( w )).

  • Explanation of single slit phenomena including bright fringes and fading of intensity.

Chapter 7: Conclusion

• Statement on the wave nature of light:

  • Light traveling through a narrow slit creates bending effects.

• Clarification on the absence of true interference patterns in single slit setups:

  • Suggestions on mathematical analysis and limitations concerning dark slit positions.

  • Formulae used are analogous to those for double slit configurations by substituting distance parameters accordingly: ( d ) replaced with ( w ) for width in single slit calculations.

physics week 6.2 part 1

his should interfere constructively. So somehow the light waves are reaching to the screen. So there is a participation that if the screen is very far. And the light wave cannot manage to reach to the screen.

dsintheta=mlambda

where d is proportional to lambda

But it is throughout the experiment we have monoclonal that passes through two steps. Produces an interference pattern of light and dark ranges. The saturation between the princess is directly related to the wavelength of light. This relation. What I have showed you that the distance between the sled. So if you vary the distance between the slit or if you are changing the wavelength, we will see the difference. Sometimes we will get the pattern. Sometimes. Likely to drag or dark bring. The upper is determined by the wavelength of the light and the separation of the slit. There is another contribution of angle. Okay.

Notes Input

Slide 1 - Lecture # 07 Introductory Physics-Electricity...

Slide 2 - Keep in mind

Keep in mind

Monochromatic light that passes through two slits produces an interference pattern of bright and dark fringes. The separation between the fringes is directly related to the wavelength of the light.

The angle at which a bright or dark fringe occurs is determined by the

wavelength of the light and the separation of the slits. The linear position of a fringe on a screen is determined by the distance from the slits to the screen.

Slide 3 - The two-slit pattern

The two-slit pattern

Conditions for Bright Fringes

(Constructive Interference) in a

Two-Slit Experiment.

Conditions for Dark Fringes

(Destructive Interference) in a

Two-Slit Experiment

Slide 4 - If light propagates at an angle θ relative to...

Slide 5 - Can we get fringe pattern with single slit?

Slide 6

Slide 7 - Single-Slit Diffraction

Single-Slit Diffraction

When light of wavelength λ passes through a slit of width W, a “diffraction pattern” of bright and dark fringes is formed. w or a are the same.

Slide 8

Slide 6

Slide 7 - Single-Slit Diffraction

Slide 8

Slide 10 - Location of dark fringe in single slit experiment

Slide 8

Slide 9 - On close inspection, the shadow of a sharp edge...

On close inspection, the shadow of a sharp edge is seen to consist of numerous fringes produced by diffraction.

Slide 10 - Location of dark fringe in single slit experiment

Slide 11

Slide 12 - Pencils create diffraction effect

• Young's Double Slit Formula

  dsin⁡θ=mλd \sin \theta = m \lambdadsinθ=mλ relates slit spacing, angle, and wavelength

Monochromatic Light Interference

Fringe separation is related to wavelength: Δx=λDd \Delta x = \frac{\lambda D}{d} Δx=dλD​

Double Slit Fringe Formula

Fringe position given by dsin⁡θ=mλ d\sin\theta = m\lambda dsinθ=mλ and yn=nλLd y_n = \frac{n\lambda L}{d} yn​=dnλL​

Fringe Position Formula

tan⁡θ=ymS \tan \theta = \frac{y_m}{S} tanθ=Sym​​, dsin⁡θ=mλ d\sin\theta = m\lambda dsinθ=mλ for small θ\thetaθ

Small Angle Approximation

For small θ \theta θ, sin⁡θ≈tan⁡θ≈θ \sin\theta \approx \tan\theta \approx \theta sinθ≈tanθ≈θ in radians

Single and Double Slit Interference

Fringe patterns arise from both double and single slit experiments: interference requires at least two waves

Single vs Double Slit Patterns

Single slit width www affects central maximum; double slit separation ddd affects fringe spacing

Single Slit Diffraction Pattern

Central fringe width depends on slit width: Wsin⁡θ=mλ W \sin \theta = m \lambda Wsinθ=mλ replaces Dsin⁡θ=mλ D \sin \theta = m \lambda Dsinθ=mλ from double slit

Single vs Double Slit

In single slit, diffraction depends on slit width www; in double slit, on slit separation ddd

Single Slit Diffraction Pattern

Central maximum has highest intensity; maxima decrease in intensity away from center

Diffraction and Intensity Pattern

Light bends through a slit; intensity fades from center: I(θ)I(\theta)I(θ) decreases with angle

Dark Fringe Spacing

All dark fringes have equal width, unlike central bright fringe

Single Slit Diffraction

Small slit width causes diffraction patterns: observe fringes if slit width a≪λa \ll \lambdaa≪λ

Single Slit Diffraction

Central maximum and patterns depend on slit width w w w or a a a

First Dark Fringe Condition

First dark fringe forms when path difference equals nλ n\lambda nλ, with diminishing intensity

Diffraction Condition Formula

\( W \sin \theta = n \lambda \ ) governs diffraction patterns

Single Slit Dark Fringes

Position of dark fringes given by y=mλDay = \frac{m \lambda D}{a}y=amλD​ for integer mmm

Dark Fringe Condition

Minima occur where light intensity is zero: I=0 I = 0 I=0

Single vs Double Slit Patterns

Single slit gives central maximum at θ=0\theta=0θ=0, double slit yields equal-width fringes

Single-Slit Diffraction Pattern

Central maximum at θ=0\theta = 0θ=0; intensity decreases for higher-order maxima

Single Slit Dark Fringe Formula

For dark fringes: ym=mλLay_m = \frac{m\lambda L}{a}ym​=amλL​, with small θ\thetaθ approximation