Determine the rms value of the electric field of the transmitted beam

• EmoryGirl
In summary, the problem involves finding the rms value of the electric field of a transmitted beam of polarized light through a polarizer at an angle of 27.5°. Using the equation I = Iocos^2theta, the correct intensity is found to be 11.7085 W/m^2, which can then be plugged into the equation for Erms to yield the final answer. However, some inconsistencies with the correct use of cosine squared in the intensity equation were encountered while solving the problem.
EmoryGirl

Homework Statement

A beam of polarized light has an average intensity of 13.2 W/m2 and is sent through a polarizer. The transmission axis makes an angle of 27.5° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.

The Attempt at a Solution

This is what I have done to try this problem:
I used Erms = square root of: [I(4pi * 10^-7)(3 x 10^8)]
I used I = Iocos^2theta
I = (13.2)(cos27.5)^2
I = 10.3856

According to the homework program I am using, the answer I have gotten is not correct...I am not sure what I am doing wrong. Thanks in advance!

I agree with your value of I=10.4 W/m^2.
Can you post your calculation of Erms?

I have finally solved it! So my Erms equation was correct. My intensity was not...
Turns out what I had to do was not square the cos...
so instead of I = Iocos227.5
the equation is:
I = Iocos27.5 = 11.7085

Which I can then plug into the equation for Erms above

yeah, I know...but our homework is on a computer program (CAPA), and after using 7 out of 10 tries on this problem I called a classmate and he said that he did it without the cos squared...so I tried it and it was finally marked correct!...not really sure what's going on with this problem!

1. What is the meaning of "rms value" in relation to the electric field of a transmitted beam?

The rms (root mean square) value of the electric field refers to the average value of the varying electric field over a period of time. It takes into account both the magnitude and the direction of the electric field, giving a more accurate representation of the overall strength of the field.

2. How is the rms value of the electric field of a transmitted beam calculated?

The rms value of the electric field is calculated by taking the square root of the mean (average) of the squared values of the electric field over a given period of time. This calculation accounts for the fluctuations in the electric field over time.

3. What are the units of measurement for the rms value of the electric field?

The units of measurement for the rms value of the electric field depend on the units of the electric field itself. If the electric field is measured in volts per meter (V/m), then the rms value will also be in V/m. Similarly, if the electric field is measured in newtons per coulomb (N/C), the rms value will also be in N/C.

4. How does the rms value of the electric field of a transmitted beam differ from the peak value?

The peak value of the electric field refers to the maximum value that the field reaches during a given period of time. It does not take into account the direction of the electric field. In contrast, the rms value considers both the magnitude and direction of the electric field, providing a more comprehensive measure of the field's strength.

5. What factors can affect the rms value of the electric field of a transmitted beam?

The rms value of the electric field can be affected by various factors such as the frequency and amplitude of the transmitted beam, as well as any obstacles or materials that the beam may pass through. Additionally, the measurement equipment and techniques used can also impact the accuracy of the rms value calculation.

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