Physics Class: Laser Diffraction and Uncertainty

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Questions and Answers

Which slit width would result in a wider diffraction pattern at a given distance?

0.2 mm (correct)

Both widths create identical patterns

Only wider slits can create diffraction patterns

0.1 mm

What does the uncertainty principle imply about the relationship between position and momentum?

Position can be precisely known without affecting momentum.

Increasing precision in measuring position decreases precision in measuring momentum. (correct)

There is no relationship between position and momentum uncertainty.

Momentum can be calculated without any uncertainty from position.

What experimental setup is recommended to maintain the intensity of the laser light during the measurements?

Switching on the laser just before measurements

Measuring in direct sunlight

Using a high-powered laser without restrictions

Using a blackened tube to cover the photcell (correct)

In the context of diffraction patterns, which equation is used to calculate the heights of the maxima?

Kirchhoff’s diffraction formula Signup and view all the answers

Which concept explains the particle-wave duality of photons in the context of diffraction patterns?

De Broglie wavelength Signup and view all the answers

What happens to the intensity pattern's width as the slit width decreases?

It spreads wider as the width of the slit decreases Signup and view all the answers

How does the momentum of blue photons compare to that of red photons?

Blue photons have higher momentum due to their shorter wavelength Signup and view all the answers

Which formula corresponds to the intensity of the diffraction pattern?

I(α) = I(0) sin(β) / β Signup and view all the answers

In a single slit diffraction experiment, what is the significance of the slit width being comparable to the wavelength of light?

It enhances the visibility of the diffraction pattern Signup and view all the answers

What is the mathematical expression for the minima of the intensity pattern in a single slit diffraction?

αn = arc sin(n / d) Signup and view all the answers

According to the Heisenberg uncertainty principle, which pairs of quantities cannot be precisely determined at the same time?

Position and momentum Signup and view all the answers

What is the primary reason why changing the laser color affects the width of the diffraction pattern?

Different colors correspond to different photon momenta Signup and view all the answers

What is represented by the variable β in the intensity formula for diffraction?

The wavelength of the light Signup and view all the answers

How does increasing the width of the slit affect the spread of momenta in the photons?

It reduces the spread in their momenta Signup and view all the answers

What is the outcome of a laser beam passing through a single slit of width d in terms of maxima?

A single maximum and several secondary maxima appear Signup and view all the answers

What effect does passing a laser beam through a slit have on the photons' properties?

It improves the accuracy of their position. Signup and view all the answers

Which variable is represented by $d$ in the uncertainty principle equation?

The width of the slit. Signup and view all the answers

How does the size of a laser beam affect its ability to pinpoint objects?

A smaller beam decreases precision in momentum. Signup and view all the answers

What principle justifies the observation that knowing a photon's position leads to an uncertainty in its momentum?

Heisenberg's Uncertainty Principle. Signup and view all the answers

In the experimental setup with a laser, slits, and a screen, what primarily determines the width of the central diffraction peak?

The wavelength of the laser light. Signup and view all the answers

What relationship does the central spot size $Y$ have with the uncertainty in momentum of the photons?

They are inversely proportional. Signup and view all the answers

What does Planck's constant $h$ signify in the context of photon behavior?

The trade-off between momentum and position uncertainty. Signup and view all the answers

When a laser beam is focused, which effect on a photon's behavior is observed?

Decreased precision in momentum. Signup and view all the answers

What does the width of the slit (d) represent in the context of photon diffraction?

The uncertainty in the position of the photons after passing through the slit Signup and view all the answers

How is the uncertainty of momentum (∆𝑝𝑦) for photons derived in the context of diffraction?

By linking momentum to the wavelength through the de Broglie relationship Signup and view all the answers

What is the relationship between the angle of the first minimum (𝛼1) and the wavelength of the photons?

The wavelength is inversely proportional to sin 𝛼1 Signup and view all the answers

In the context of a photon passing through a slit, what represents the uncertainty in its velocity component in the y-direction?

The intensity distribution in the ensuing diffraction pattern Signup and view all the answers

How is the mass of a photon described in the context of the equations related to momentum?

Photons have a rest mass of zero, but momentum can still be defined Signup and view all the answers

Which equation shows the relationship between the uncertainties in speed and their respective wavelengths for photons?

ℎ/𝜆 = ∆𝑝𝑦 Signup and view all the answers

What role does the first minimum play in defining the uncertainty of the velocity component (∆𝑣𝑦)?

It establishes the reference point for measuring angle and velocity Signup and view all the answers

What does the de Broglie relationship imply about the wavelength of photons?

It links the wavelength inversely to the momentum of the photon Signup and view all the answers

Why is the uncertainty principle significant in the context of photons passing through a slit?

It highlights the trade-off between precision in position and momentum Signup and view all the answers

Which of the following statements is true regarding the properties of photons after passing through a slit?

Photons exhibit both position and momentum uncertainty Signup and view all the answers

Study Notes

Apparatus

Laser, He-Ne, λ=632.8 nm
Diaphragm, 2 single slits, 0.1 mm, 0.2 mm
Diaphragm holder
Photoelement
Universal measuring amplifier
Optical profile-bench, 1500 mm
Base optical profile-bench, adjustable
Slide mount optical profile-bench, h 80 mm

Background

Position and Momentum of Light: A laser beam is a directed beam of light containing many photons. Each photon follows quantum mechanics rules, including the Uncertainty Principle.
Uncertainty Principle: It's impossible to know both the position and momentum of a photon precisely at the same time.
Laser Beam Characteristics: Laser beams have well-defined momentum; this allows them to remain relatively small over long distances because their position is known precisely.

Diffraction and Uncertainty Principle

Diffraction: When a laser beam passes through a slit (of width 'd'), it spreads out (forming a diffraction pattern) as it travels a distance to the screen 'L'.
Uncertainty in Momentum: Passing a beam through the slit affects its momentum. The smaller the slit, the greater the uncertainty in momentum.
Uncertainty Principle Relation: The uncertainty in position (Δy) and momentum (Δp) are related by: Δy. Δp ≥ h, where 'h' is Planck's constant.
Relationship Between Slit and Position: Smaller slits lead to more precise position information but increase the uncertainty in momentum.

Observation from Wave Pattern Viewpoint

Single Slit Diffraction: A monochromatic (single-color) coherent light beam passing through a single slit creates a diffraction pattern with a principal maximum and secondary maxima on a screen.
Intensity Formula: The intensity of the diffraction pattern (as a function of the angle of deviation 'a') is given by Kirchhoff's diffraction formula: I(a) = I(0)(sin β/β)², where β = πd sin a/λ (and λ is wavelength).
Intensity Minima: Intensity minima occur at angles where aₙ = arcsin(nλ/d), where 'n' = 1, 2, 3,...

Quantum Mechanics Treatment

Uncertainty Relation Confirmation: The Heisenberg uncertainty principle states that two conjugate quantities (like position and momentum) cannot both be known with perfect accuracy.
Photon Momentum: The momentum of a photon relates to its wavelength (p = h/λ).
Relationship Between Velocity and Uncertainty: The uncertainty in momentum is related to the uncertainty in the photon's velocity component and the width of the single slit.
Uncertainty Relationship Equation: The uncertainty in position (Δy) and momentum (Δp) are linked to the width of the slit and to the wavelength by: Δy × Δp ≥ h.

Experimental Setup and Procedure

Diffraction Pattern Measurement: Measure the intensity distribution in the diffraction pattern from varying slit widths (0.1 mm and 0.2 mm) using a photo-cell.
Plotting Intensity vs Position: Plot the intensity of the diffraction pattern as a function of position on a graph.
Laser Beam Considerations: The laser beam should be stabilized for consistent measurements; consider the use of protective tubes if necessary.

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Description

Test your understanding of laser diffraction and the Uncertainty Principle in physics. This quiz covers key concepts such as the characteristics of laser beams, their behavior through slits, and the implications of quantum mechanics on light. Perfect for students studying optical phenomena in physics classes.