Which of the following exerts the largest amount of radiation pressure? a) a 1-mW laser pointer

step 1 Here we're going to look at radiation pressure. And what this is is it is due to change in momen

Which of the following exerts the largest amount of...

Key Concepts

Radiation Pressure

Radiation pressure is the force exerted per unit area by electromagnetic radiation when it interacts with a surface. This pressure arises because photons, despite having no rest mass, carry momentum which can be transferred to objects upon absorption or reflection. Understanding radiation pressure is crucial for topics such as solar sails, laser manipulation of small particles, and astrophysical processes.

Intensity and Power Distribution

Intensity is defined as the power per unit area of a beam of radiation. In scenarios involving focused beams, such as lasers or spotlights, the amount of radiation pressure depends on how the power is distributed over a given area. A beam with a smaller spot size concentrates its power and thus increases the intensity, which in turn raises the radiation pressure exerted on the surface.

Beam Geometry and Spot Size

The geometry of a light beam, including the size of its spot or focal area, directly influences the intensity and the resulting radiation pressure. Smaller spot sizes result in higher intensities because the same amount of power is focused on a smaller area, making this a key factor when comparing the effects of different light sources or configurations.

Inverse Square Law

The inverse square law describes how intensity decreases with distance from a point source. For isotropically radiating sources, the intensity decreases as the square of the distance increases. This principle is important when comparing sources of radiation at different distances, as even with similar power outputs, the effective intensity (and thus the radiation pressure) can vary significantly with distance.

Transcript

00:01 Here we're going to look at radiation pressure.

00:03 And what this is is it is due to change in momentum of an electromagnetic wave when it runs into some sort of material.

00:15 And here we are going to assume that our material is an absorber, a perfect absorber for the sake of argument.

00:27 And the idea is we have an electromagnetic wave, impinging on that material and that material will experience both a force as well as absorb energy from the electromagnetic wave.

00:54 The quantity that tells you the energy flow inside of that wave is called the pointing vector and usually we are interested in the average of that.

01:08 So the pointing vector oscillates just like the wave does in time and in space.

01:15 But here we are interested in measuring just its average intensity, if you will, in units of watts per meter squared.

01:26 So it is a flow of energy per unit area, the pointing vector.

01:32 The radiation pressure is related to that.

01:36 Let's write that with a big p, so it doesn't look like momentum and i'll give it subscript rad for radiation pressure.

01:45 Is the average value of the pointing vector divided by the speed of light? and this will be, if everything is in si units, including the s, this should be in newton's per meter squared.

02:05 So yes, light can create pressure.

02:09 And as we'll see, it is this pressure that people utilize.

02:12 When they build an optical tweezer.

02:17 And we'll get into that.

02:19 Because what we will be doing is comparing the radiation pressure that is experienced in the path of a laser to that of a light bulb.

02:43 And the difference between those is in the s.

02:47 So we can basically ignore the speed of light in our radiation pressure.

02:52 And so we are really going to compare the average pointing vector, sometimes called the flux or the irradiance in watts per meter squared.

03:13 And the difference between them is that the laser beam is collimated.

03:23 So let's first of all take a look at a laser beam.

03:27 And it hits the wall, which is going to absorb the light.

03:33 And feel a force.

03:36 And let's assume that all the energy is in a spot that is two millimeters in diameter.

03:53 And we have measured the power in the laser beam as one milliwatt or 10 to the minus three watts.

04:04 Then that irradiance s is simply 10 to the minus three watts, by the area of that little spot pi times radius squared with the radius.

04:24 Let's see, i think we have 2 milawatts in our laser beam.

04:28 Now it is 1 milamatt.

04:30 So it is 2 millimeters in diameter.

04:34 That's the 2.

04:36 So the radius is equal to 10 to the minus 3 meters.

04:42 And working out what that s is, it is of the order...

Please give Ace some feedback