Review questions for HW 2

1. At what incidence angle an EM wave can be 100% transmitted without reflection at a boundary? What is polarization of the wave under this condition?

P-polarization will be transmitted 100% at Brewster angle.

2. How do you call an oblique EM wave that propagates toward a boundary and has its magnetic field parallel to the boundary?

TM or p-polarization.

3. Under what condition on the refractive indices so that totally internal reflection is possible?

n_1 > n_2

4. What is the fraction of the input power of an EM wave is not being transmitted at glass-air interface? Assume the wave is normal to the interface.

Not transmitted => reflected. Fraction of power reflected = R =  (n_2 - n_1 )^2 / (n_2 + n_1 )^2
R = 0.5^2/2.5^2 = 0.04. And T = 1 - R = 0.96.

5. You have 2 laser beams, with beam radii of 10 micron and 1mm. Which one has larger divergence angle?

10 micron

6. For a laser beam with the following beam shape at the laser, which dimension of the beam with be longer when it is far from the laser?

x dimension

7. At what distance from the laser you need to consider the beam expansion?

z > z_o

8. For a Gaussian beam, at what field amplitude is the beam waist (radius) is defined?

1/e of the max E-field amplitude

9. What is the optical path difference for a Michelson interferometer with one arm having an d_1 long air column and another arm having a d_2 long column with refractive index n_2? (see diagram below)

2(n_2*d_2 - d_1)

10. Find the condition for constructive interference for the interferometer in question 9.

2(n_2*d_2 - d_1)*2*pi/lambda_o = 2*m*pi => n_2*d_2 - d_1 = m*lambda_o/ 2

11. What is the function of an interferometer?

Convert phase info (modulation) to intensity info (modulation)

12. What optical effect is used in making holograms?

Interference

13. What conditions are required to reconstruct an image from an ordinary hologram?

The reference beam is from a coherent light source (i.e. laser) with the same wavelength as the one used in recording the hologram. The reference should travel in the same direction as that of the reference in hologram recording.