A typical laser used in introductory physics laboratories produces a continuous beam of light about 1.0 mm in diameter. The average power of such a laser is 0.75 mW.
(i) What is the average intensity?
(ii) What is the peak intensity?
(iii) What is the average energy density of this beam?
(iv) If the beam is reflected from a mirror, what is the maximum force the laser beam can exert on it?
(v) Describe the orientation of the laser beam relative to the mirror for the case of maximum force.
Damon?? can you help me out on this one please
I have this same question, hope you get the answer
well, it is late but I might be able to point a direction
average intensity
= average power / (pi r^2)
Peak = twice average power if a sine wave
[ average of sin^2 = (1/2) ]
energy density usually in Joules per square centimeter where it hits I assume per second. That would be the power * c /pi r^2
The maximum force is when the light is reflected straight back, changing in momentum from plus to minus
The maximum force is twice the momentum of the beam times c which is how much hits per second.
The relation between the energy and the momentum is
E = p c where p is momentum
so our momentum density here is our energy density/c
To answer these questions, we need to use some formulas from optics and energy analysis. Let's break it down step by step:
(i) Average intensity:
Intensity is defined as power per unit area. The formula to calculate average intensity is:
Average Intensity = Average Power / Area
Given that the average power of the laser is 0.75 mW and the laser beam has a diameter of 1.0 mm, we can calculate the area using the formula for the area of a circle:
Area = π * (Diameter/2)^2
Substituting the values into the formula, we get:
Average Intensity = 0.75 mW / [π * (1.0 mm / 2)^2]
= 0.75 mW / [π * (0.5 mm)^2]
= 0.75 mW / [π * (0.5^2) mm^2]
= 0.75 mW / (π * 0.25 mm^2)
= 0.75 mW / 0.785 mm^2
≈ 0.955 mW/mm^2
Therefore, the average intensity of the laser beam is approximately 0.955 mW/mm^2.
(ii) Peak intensity:
The peak intensity of light in a continuous wave laser beam is double the average intensity. Therefore,
Peak Intensity = 2 * Average Intensity
≈ 2 * 0.955 mW/mm^2
≈ 1.91 mW/mm^2
So, the peak intensity of the laser beam is approximately 1.91 mW/mm^2.
(iii) Average energy density:
The average energy density is the average energy per unit volume. In this case, we need to find the energy per unit volume.
Given that energy is the product of power and time, the formula for energy density is:
Average Energy Density = Average Power / Volume
The volume of the laser beam can be calculated using the formula for the volume of a cylinder:
Volume = π * (Diameter/2)^2 * Length
Since no length information is given in the question, we cannot determine the average energy density without it.
(iv) Maximum force exerted on a reflecting mirror:
When the laser beam is reflected from a mirror, it exerts a force on the mirror due to the transfer of momentum. The force exerted by the light can be calculated using the formula:
Force = 2 * Average Power / Speed of light
Given that the average power is 0.75 mW and the speed of light is approximately 3.0 x 10^8 m/s, we can substitute these values into the formula:
Force = 2 * 0.75 mW / 3.0 x 10^8 m/s
= 1.5 mW / 3.0 x 10^8 m/s
≈ 5 x 10^-9 N
Therefore, the maximum force the laser beam can exert on a mirror is approximately 5 x 10^-9 N.
(v) Orientation of the laser beam relative to the mirror for maximum force:
To achieve maximum force on the mirror, the laser beam should be incident normally (perpendicular) to the mirror surface. In other words, the laser beam should make a 90-degree angle with the mirror surface.
Please note that these answers are based on the information provided and the assumptions made.