# Maxwell Law of electromagnetic waves

1. (a) (5 pts) State the equations of maxwell Law of electromagnetic waves.
(b) (10 pts) Show that the equation described below satisfy Maxwell’s
second order differential equation of electromagnetic wave
Ey(x, t) = 5(N/C) sin(107 x – 3•1015t) k
where t is in seconds and x is in meters.
.
(c) (5pts) What is the direction and maximum value of the magnetic field
strength of the wave described by the above equation?
2. (16 pts) Young’s double-slit experiment is performed with 620-nm light
and a distance of 1.00 m between the slits and the screen. The 8th
interference minimum is observed 5.26 mm from the central maximum.
Determine the spacing of the slits.
3. (17 pts) An unpolarized light 4 W/m2
in intensity is passed through a
polarizer and two other analyzers as depicted below. The transmission
axes are θ1=20
o
, θ2 = 10
o
and θ3 = 70
o with respect to the vertical axis.
What is the intensity of the light after it passes the last analyzer?
Polarizer 1st analyzer 2nd analyzer
θ1 θ2 θ3
4. (16 pts) Use Ray Tracing Diagram to locate the position and height of the
image by a diverging lens. Give percent error with the theoretical
calculation using lens makers equation. The focal length of the lens is 5
cm, the distance of the object from the lens is 10 cm and the height of the
object is 4 cm.
5. (16 pts) Calculate the minimum thickness of a soap-bubble film that
results in constructive interference in the reflected light if the film is
illuminated with light whose wavelength in free space is λ = 620 nm.
6. (15 pts) A grating with 50 grooves/mm is used with an incandescent light
source. Assume the visible spectrum to range in wavelength from 400 nm
to 700 nm. In how many orders can one see (a) the entire visible spectrum
and (b) the short-wavelength region of the visible spectrum?

Sample Solution

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