## Reflection and Transmission at Normal Incidence

 Electromagnetic waves pass from a linear material with index of refraction (n1=1.5) into a linear material with an index of refraction, n2. The waves move perpendicular (normal) to the interface between the materials. How do the phases of the incident, reflected, and transmitted waves and the relative amounts of average reflected and transmitted power per unit area change as n2 changes?

QUESTIONS

(Score is number right minus number wrong.)

A proper boundary condition at the the interfaces is that the component of the transmitted electric field parallel to the interface equals the parallel component of the
incident electric field.
reflected electric field.
sum of the incident and reflected electric field.
The correct boundary condition for the parallel component of electric field is expressed mathematically as,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
The condition of Equation (6f) must be satisfied
at all values of z and at all times t.
at z=0 and at all times.
at z=0 and at t=0 only.
If the parallel component of the incident electric field remains in phase with the transmitted component of electric field at the interface, the parallel component of the incident electric field must always remain in phase with the parallel component of the reflected ELECTRIC field at the interface.
True.
False.
If the parallel component of the incident electric field remains in phase with the reflected component of electric field at the interface, the direction of the Poynting vector can be used to determine the correct phase of the reflected MAGNETIC field at the interface.
True.
False.
The correct boundary condition for the parallel component of magnetic field is expressed mathematically as,
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)
Equation (6e)
Equation (6f)
At this point we assume that the magnetic permeabilities of the two materials are the same. Under these conditions, at z=0, we can cancel the time dependence on both sides and solve for the relative (complex) amplitudes of the electric field. The result is given as Equation (7).

For complex numbers in polar form to be equal, the modulus and amplitudes must separately be equal. See Equation (1). According to Equation (7) the phase of the reflected electric field at the interface must always be the same as that of the incident electric field, no matter what the indices of refraction are which determine the modulus.
True.
False.
The minus sign that can occur between the complex reflected amplitude and the complex incident amplitude (See Equation (7).) when n2 > n1 can be interpreted as a 180 degree shift in phase between incident and reflected electric fields at the interface. (See Equation (8).) (See the animation.)
True.
False.
The transmitted electric field is always 180 degrees out of phase with the incident electric field at the interface. (See the animation.)
True.
False.
As one crosses the interface, what does NOT change for the transmitted wave relative to the incident wave? (See the animation.)
wavelength.
speed.
frequency.
amplitude.
Which changes for the reflected wave relative to the incident wave? (See the animation.)
wavelength.
frequency.
amplitude.
To maximize the average transmitted power, make (See the animation.)
n2 less than n1.
n2 = n1.
n2 greater than n1.
For the same difference between n1 and n2, it does not matter for the average transmitted power whether n2 is less than n1 or n2 is greater than n1. (See the animation.) (See Equations (11-12).)
True.
False.
To decrease the amplitude of the transmitted wave, (See the animation.)
increase n2 relative to n1.
decrease n2 relative to n1.
To decrease the speed of the transmitted wave, (See the animation.)
increase n2 relative to n1.
decrease n2 relative to n1.
To decrease the wavelength of the transmitted wave, (See the animation.)
increase n2 relative to n1.
decrease n2 relative to n1.
To decrease the amplitude of the reflected wave, (See the animation.)
increase n2 relative to n1.
decrease n2 relative to n1.
EQUATIONS

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