Photon Momentum (Micro Lesson for AP Physics)

Summary

In this humorous physics lesson, the instructor starts with a light-hearted joke about light having mass, which leads to a deeper discussion on the properties of light. The confusion arises from the common formula P = mv, which doesn't apply to light since it's massless. The instructor clarifies that special relativity allows massless objects like light to have momentum through a loophole. The correct formula to calculate the momentum of a photon is given by P = h/λ, where h is Planck's constant and λ is the wavelength of light in meters. The lesson concludes with the reminder that while a single photon's momentum is minuscule, it can theoretically propel a solar sail, emphasizing the importance of understanding the correct physics behind light's behavior.

Takeaways

• 😀 Light has momentum despite having no mass.
• 😀 The joke about light not being Catholic confused students about light's properties.
• 😀 Light having momentum seems contradictory to the equation P = MV.
• 😀 For objects traveling close to the speed of light, special relativity must be used.
• 😀 Special relativity allows massless objects like photons to have momentum.
• 😀 The formula for photon momentum is H over lambda.
• 😀 H represents Planck's constant (6.626 x 10^-34 joule-seconds).
• 😀 Lambda is the wavelength of light in meters (conversion from nanometers is necessary).
• 😀 The momentum of a single photon is extremely small, hence we don't feel light's push.
• 😀 A large solar sail can be propelled by light due to the impulse from photon momentum.

Q & A

What is the main topic of the physics joke shared in the transcript?

The main topic of the physics joke is the concept of light having mass, which is humorously refuted by the teacher, only to later explain that light does have momentum without mass.

Why did the teacher's joke confuse the students?

The joke confused the students because it contradicted their understanding that light has momentum, which they believed implied that light also has mass.

What is the correct formula to determine the momentum of a photon?

The correct formula to determine the momentum of a photon is momentum equals Planck's constant (H) divided by the wavelength (lambda) of the light, expressed as p = h / λ.

Why is the classical formula P = mv not accurate for calculating the momentum of a photon?

The classical formula P = mv is not accurate for a photon because it assumes a mass (m) that a photon does not possess. For objects moving at or near the speed of light, special relativity must be considered, which allows for massless objects to have momentum.

What is the significance of the term 'special relativity' in the context of the script?

Special relativity is significant because it provides a theoretical framework that allows for the possibility of massless particles, like photons, to have momentum, which would otherwise be impossible under classical physics.

Why does the teacher say that light having momentum is a 'loophole'?

The teacher refers to it as a 'loophole' because, according to classical mechanics, a massless object cannot have momentum. However, special relativity provides an exception to this rule, allowing light, which is massless, to possess momentum.

What is Planck's constant and what is its value?

Planck's constant (H) is a fundamental physical constant that describes the scale of quantum effects. Its value is approximately 6.6 x 10^-34 joule-seconds.

Why is the momentum of a single photon considered to be extremely small?

The momentum of a single photon is extremely small because Planck's constant is very small, and the wavelength of visible light is relatively large. This results in a very small value when calculating momentum using the formula p = h / λ.

What is a solar sail and how could it be propelled by light?

A solar sail is a proposed method of spacecraft propulsion that uses the pressure exerted by the momentum of photons from the Sun to propel a sail. The momentum of light bouncing off the sail could theoretically propel it forward.

Why doesn't the pressure we feel when light shines on us indicate a significant momentum transfer?

The pressure we feel from light shining on us is minimal because the momentum of individual photons is extremely small. The collective effect of a vast number of photons is required to produce a noticeable force.

What is the importance of converting nanometers to meters when using the formula for photon momentum?

Converting nanometers to meters is important because the formula for photon momentum uses the wavelength in meters. Wavelengths are often given in nanometers in many contexts, but for the calculation, the correct unit is essential to avoid errors.

How does the concept of momentum in the context of light relate to the broader understanding of quantum mechanics?

The concept of momentum in the context of light is a fundamental aspect of quantum mechanics, as it demonstrates the dual wave-particle nature of light. Understanding that light can have momentum without mass is a key insight into the principles of quantum theory.