- #1

Taylor_1989

- 402

- 14

- Homework Statement
- A plane electromagnetic wave is traveling in a vacuum in the positive Z direction and is normally incident on a planar glass of refractive index 1.50 and finite thickness. For normal incidence at a dielectric interface, the reflection and transmission coefficients of intensity are:

##R=\frac{(n_2-n_1)^2}{(n_2+n_1)^2}##

##T=\frac{(4n_1n_2)^2}{(n_2+n_1)^2}##

When the wave enters the glass plate it reflects from both the front and back surfaces of the interface. Considering these two contributions only, show that the total reflected intensity is approximately 7.7% of the incident intensity.

- Relevant Equations
- Contained within the question

Diagram

Calculations as follows

$$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{I_{R_1}+I_{R_2}}{I_0}*100=\frac{R*I_0+(R*T)*I_0}{I_0}$$

Subbing in the relevant equations given in the question

$$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{(n_2-n_1)^2}{(n_2+n_1)^2}(1+\frac{(4n_1n_2)^2}{(n_2+n_1)^2})*100$$

Now by subbing in the numerical values into my above eqaution I get a percentage of ##7.84 \%## and the question states that it should be ##\approx 7.7%## thus I am not sure my working are correct but can't really understand why as there no other reflection that I can account for, I did think maybe it ment a reflection off the first mirror again but adding that into the above calculations I get ##8\%## which it larger than my original. Have I missed something in my calculation?

Calculations as follows

$$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{I_{R_1}+I_{R_2}}{I_0}*100=\frac{R*I_0+(R*T)*I_0}{I_0}$$

Subbing in the relevant equations given in the question

$$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{(n_2-n_1)^2}{(n_2+n_1)^2}(1+\frac{(4n_1n_2)^2}{(n_2+n_1)^2})*100$$

Now by subbing in the numerical values into my above eqaution I get a percentage of ##7.84 \%## and the question states that it should be ##\approx 7.7%## thus I am not sure my working are correct but can't really understand why as there no other reflection that I can account for, I did think maybe it ment a reflection off the first mirror again but adding that into the above calculations I get ##8\%## which it larger than my original. Have I missed something in my calculation?