Practice 04

1. A plane polarized EM wave propagates through a polymer. Such waves obey a similar wave equation to that found for free space. The wave has a magnetic field vector, ������⃗=[(−1.2����̂)∗sin(��������+��������)] μT, with frequency ����=7.61×1014 Hz and wavenumber ����=1.61× 107 ����−1. Find the speed of the wave, the electric field vector, and the direction of propagation of the wave.

2. Coherent green light of wavelength 650 nm illuminates two narrow slits in a screen. The slits are separated by 0.0.8 mm. A thin transparent plastic film (index of refraction 1.3) covers one slit. The light from the slits reaches a screen 1.0 m away. Starting from first principles, find the minimum thickness of the film that turns the third-order dark fringe (without the film) into a bright fringe (with the film).

3. The magnetic field of a plane-polarized electromagnetic wave is given by in SI units. The field vector is ������⃗=����(����,����)(����̂+����̂)√2 . Find the average power per square meter carried by the EM wave. Write the electric field vector. Compute the Poynting vector.

4. An aquarium contains a 5-cm layer of water (n = 1.333) floating on top of carbon tetrachloride (n = 1.461). If the angle of incidence into the water from the carbon tetrachloride is 20°, what is the angle of refraction into the air?

5. A plane convex lens is made of glass (n = 1.5) with one flat surface and the other having a radius of 20 cm. What is the focal length (in cm) of the lens? Where does the image form for an object 4.0 cm away? If the image is 6.0 cm tall, what is the magnification and size of the object? Is it real or virtual; upright or inverted?

6. The figure shows two point sources of light, A and B. B emits light waves that are +πradians out of phase with the waves from A. A is 3λfrom P. B is 5λfrom P. (λis the wavelength.) Find the phase difference between waves arriving at P from A and B. What kind of interference does this situation lead to at P?

7. Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45.0° to the preceding filter. What percentage of light gets through