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he intensity of a cylindrical laser beam is 0.800W/m2. The cross-sectional area of the beam is3.0×10-4W/m2 and the intensity is uniform across the cross section of the beam. (a) What is the average power output of the laser? (b) What is therms value of the electric field in the beam?

Short Answer

Expert verified

a. The average power output of the lase is 2.4×10-4W.

b. Therms value of the electric field of the beam is 17.4V/m.

Step by step solution

01

Define the intensity ( I ) and define the formulas.

The power transported per unit area is known as the intensity ( I ) .

The formula used to calculate the intensity ( I ) is:

I=PA

Where, Ais area measured in the direction perpendicular to the energy and Pis the power in watts.

And also, I=12ε0cEmax2. Where, Iis the intensity in W/m2and cis the speed of light that is equal to 3.0×108m/sand also

Erms=Emax2ε0=8.85×10-12C2/N·m2

So, therms value of the electric field in terms of intensity ( I ) is written as

Erms=Iε0c

02

Determine the average power.

Given that,

I=0.800W/m2A=3×10-4m

The formula used to calculate the intensity ( I ) is:

I=PavgAPavg=IA

Substitute the values

P=0.8003×10-4=2.4×10-4

Hence, average power output of the lase is 2.4×10-4.

03

Determine the value of electric field.

The rmsvalue of the electric field is

Erms=Iε0c

Substitute the values

Erms=0.8008.85×10-123×108=17.4V/m

Hence, the role="math" localid="1664349239967" rmsvalue of the electric field of the beam is role="math" localid="1664349211670" 17.4V/m.

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