A beam of polarized light with an average intensity of 17.1 W/m2 is sent through a polarizer. The transmission axis makes an angle of 27° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.
Answer in N/C
half that power is in the E field.
1/2 * 17.1= epsilion*E^2/2
solve for E.
Now after the polarizer, only cos27 gets thru.
Efinal=E cos27
To determine the rms value of the electric field of the transmitted beam, we can use the relationship between the intensity and electric field for polarized light.
The intensity of polarized light is given by the equation:
I = (1/2) * ε₀ * c * E₀²
Where:
- I is the intensity of the light (in W/m²),
- ε₀ is the vacuum permittivity (8.85 × 10⁻¹² F/m),
- c is the speed of light in a vacuum (3.00 × 10⁸ m/s),
- E₀ is the rms value of the electric field (in N/C).
We can rearrange the equation to solve for E₀:
E₀² = (2 * I) / (ε₀ * c)
E₀ = sqrt((2 * I) / (ε₀ * c))
Now, let's apply the given values to calculate the rms value of the electric field of the transmitted beam:
I = 17.1 W/m²
ε₀ = 8.85 × 10⁻¹² F/m
c = 3.00 × 10⁸ m/s
E₀ = sqrt((2 * 17.1) / (8.85 × 10⁻¹² * 3.00 × 10⁸))
Calculating the square root:
E₀ ≈ 3.66 x 10⁶ N/C
Therefore, the rms value of the electric field of the transmitted beam is approximately 3.66 × 10⁶ N/C.