Wave Optics problems

1. A cylindrical wave propagates in a medium with a refractive index of in r direction and the polarization is perpendicular to the π‘Ÿβƒ— direction, as given by equation below

𝐸⃗(π‘Ÿ,𝑑)=400πœ‹βˆšπ‘Ÿ.𝑒𝑖(πœ”π‘‘βˆ’15πœ‹βˆ—106π‘Ÿβˆ’0.2πœ‹)πœƒΜ‚ (π‘‰π‘š)

a) What is the amplitude of this light wave at π‘Ÿ=100 π‘š?

b) What is the frequency of this light wave?

c) What is the intensity of this light wave at π‘Ÿ=100 π‘š?

d) What is the light power of this light wave at π‘Ÿ=100 π‘š?

2. A linearly polarized light is incident into a lower refractive medium with a refractive index 1.33 from a higher refractive index medium with a refractive index 1.7. The polarization is in parallel to the incident plane. Please calculate

a) The percentage of transmitted light intensity if the incident angle is zero.

b) The minimum incident angle so that the light intensity can be 100% reflected.

c) The incident angle so that the incident light intensity can be 100% transmitted.

d) The incident angle so that the incident light intensity can be 50% transmitted. (Hint: You may use computer software such as Matlab, Mathcad, to do this).

e) If the incident angle is 60 deg and the incident wavelength is πœ†=0.5 πœ‡π‘š, what will be the penetration depth?

3. In Young’s double slit interference experiment, we assume that the distance between two identical slits is and the distance between the slits and observation screen is . If the wavelength of the incident light is πœ†=500 π‘›π‘š π‘Žπ‘›π‘‘ π‘ π‘π‘’π‘π‘‘π‘Ÿπ‘Žπ‘™ π‘€π‘–π‘‘π‘‘β„Ž π‘œπ‘“ π‘‘β„Žπ‘’ π‘€π‘Žπ‘£π‘’π‘™π‘’π‘›π‘”π‘‘β„Ž 𝑖𝑠 0.1 π‘›π‘š, please calculate followings:

(a) The vertical location of the third minimum.

(b) The first location where the intensity of the light is half of the maximum.

(c) What will be happened if the width of one of the slits is doubled?

(d) What is the maximum allowed optical path difference between the beams from two slits.

4. A monochromatic light with wavelength is used to illuminate a single slit. Assume that the width of slit is . The distance between slit and the observation screen is L.

(a) Please sketch the light intensity distribution for 𝐿<0.3 π‘šπ‘š.

(b) Please sketch the diffraction pattern at the location L = 10 mm.

(c) Please sketch the light intensity distribution for L = 5000 mm.

(d) What is the full width of the central spot for L = 5000 mm.

5.

a) What is the definition of Rayleigh resolution?

b) A microscope objective has an aperture 1mm and a focal length of 1mm. If the illumination wavelength is 0.4 micron and the sample is immersed in a liquid with a refractive index of 1.33, what is the resolution of this microscopic system?

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