Question

He-Ne lasers are often used in physics demonstrations. They produce light of wavelength 633nm and a power of 0.650mW spread over a cylindrical beam 1.35mm in diameter (although these quantities can vary).


Part A
What is the intensity of this laser beam?
I=___________W/m^2


Part B
What is the maximum value of the electric field?
Emax=__________V/m


Part C
What is the maximum value of the magnetic field?
Bmax=__________uT


Part D
What is the average energy density in the laser beam?
Uav=____________J/m^3

Answer 1

Concepts and reason

The concept used to solve this problem is intensity of laser beam, maximum value of electric and magnetic field, and average energy density in the laser beam.

First use the relation between power and area to calculate the intensity of the laser beam.

Use the intensity of the laser beam and speed of the light to calculate the maximum value of electric field. Finally by this electric field calculate the magnetic field and average energy density.

Fundamentals

Expression for the intensity of the laser beam is,

Here, Iis the intensity of the laser beam, P is the power, and A is the surface area.

Expression for the maximum value of the electric field is,

Here, is the maximum value electric field and c is the speed of the light.

Expression for the maximum of the magnetic field is,

Here, is the maximum of the magnetic field.

Expression for the average energy density in the laser beam is,

Here, is the average energy density in the laser beam.

(A)

Expression for the radius of the cylindrical beam is,

Here, is the radius of the cylindrical beam and is the diameter of the cylindrical beam.

Substitute for d.

Expression for the surface area of the cylindrical beam is,

Here, A is the surface area of the cylindrical beam.

Substitute for r.

Expression for the intensity of the laser beam is,

Substitute for P and for A.

(B)

Expression for the maximum value of the electric field is,

Substitute for c, for , and for I.

(C)

Expression for the maximum of the magnetic field is,

Substitute for and for c.

(D)

Expression for the average energy density in the laser beam is,

Substitute for an d for .

Ans: Part A

The intensity of the laser beam is .

Part B

The maximum value of the electric field is .

Part C

The maximum of the magnetic field is .

Part D

The average energy density in the laser beam is.