Answered: 7. The Numerical Aperture, NA, of a… | bartleby

Related questions

Question

7. The Numerical Aperture, NA, of a waveguide is defined as no sin A where nд is the refractive
index of the material from which the light enters the waveguide and is the maximum acceptance
angle, as shown in Q3. Apply trigonometry to the figure in Q3 and show that the Numerical
Aperture is:
√√n²-n²
NA =

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

4. a. Determine the size of the Airy disk (in m) found at the center of a 4.00-cm diameter lens, with a focal length of 15.0 cm. Assume the incident light wavelength is the middle of the visible spectrum = 550. nm. b. In observational astronomy, we assume that stars, being so far away, are point sources of light, and that the image of a star in a telescope eyepiece is therefore also a point. Given that the average human near-field resolution is 0.10 mm, does your result in part a justify this assumption? Explain your answer, using the value from part a. c. Assume that the objective lens diffraction limit is the only one that matters on a telescope (actually a good assumption, not justified here). What is the angular size (in radians) of the smallest object that can be truly observed as a disk on the 4.00-cm telescope in part a? Can Jupiter (maximum angular size = 51 arc-seconds) be seen as a disk through this telescope? Note that real telescopes have glass or mirror imperfections which…
Problem 1: You want to test a special watertight monochromatic light source in an un- derwater environment. If the light source shines its beam of electromagnetic radiation into your eyes when you and the light source are above the water, with both your eyes and the light source immersed in air, the beam appears to your eyes to have a deep violet color. The index of refraction of water is about 1.33 What color, if any, would your eyes perceive the beam to have when you and the light source are submerged in water – and why? (A) No color. The beam would become invisible under water because its wavelength in water is shorter than in air, corresponding to a wavelength of ultra-violet light. The beam's wavelength in the water determines its visibility to the eye under water, and ultra-violet light is not visible to the human eye. (B) Same color as in air, above the water, i.e., deep violet. Under water, the beam would have the same wavelength as in air. The beam's wavelength in the water…
An extremely thin sheet of glass is being inspected at the laboratory. Illuminated by white light at near-normal incidence, the film-like sheet is 0.371 µm thick and has air on both sides. If the glass has a refractive index of 1.66, what wavelength of visible light (in nm) does it reflect most strongly? (The wavelengths of visible light range from 400 to 700 nm.) nm
** 38. Two plastic plates (index of refraction n = 1.3) are separated by an air gap of 0.9 µm. Analyze the reflections of light of wavelength 600 nm and conclude whether it will be brightly reflected or not. 0.9 um gap ** 39. The air gap in the previous problem is now filled with a mineral oil whose index of refraction is n = 1.5. Analyze the reflections of light of wavelength 600 nm and conclude if it will be brightly reflected or not.
An ideal polarizing sheet transmits 90% of the incident partially polarized light. The polarizing sheet is now rotated through 45 degrees; during the rotation process the transmitted light monotonically decreases in intensity. What fraction of the incident intensity now passes? O a. 0% O b. between 40% and 90% O c. Between 50% and 80% O d. 50% O e. Between 0 and 50%
33. You have a laser (a monochromatic light source) and want to estimate the wavelength. You decide to use a reflective diffraction grating to do this. The light is incident on the grating at 20 degrees with respect to normal. Using a grating with a groove distance of 5 um, the first-order diffraction, is found at an angle of -12.5 degrees. Determine the wavelength of the source. a) 500 nm b) 628 nm c) 808 nm d) 946 nm e) None of the above 34. In Raman spectrometry, Stokes lines have a) lower energy than that of anti-Stokes scattering. b) equal energy to that of anti-Stokes scattering. ) higher energy than that of anti-Stokes scattering d) none of the above 35. Upon ionization of phenol in aqueous solution, maximal UV absorbance changes to longer wavelength. a) True b) False 36. It takes longer time to observe fluorescence than phosphorescence. a) True b) False 37. The vibrational motion of C-H stretching in ethylene as in the figure can be detected by a) IR. b) Raman. c) IR and Raman.…
A diffraction grating with unknown number of lines per mm is illuminated by light at a wavelength = 633 nm and the first order diffraction pattern is seen at an angle B = 50.0°. Light of a second wavelength is shone onto the grating, whose second order diffraction pattern is seen at y = 60.0°. What is the wavelength of this second beam? 358 nm 392 nm 716 nm 548 nm 272 nm
A physicist is calibrating a spectrometer that uses a diffraction grating to separate light in order of increasing wavelength (?A,?B, and ?C). He observes three distinct first-order spectral lines at the following respective angles ?m (where m denotes order). ?1 = 12.8°, ?1 = 14.2°, ?1 = 15.0° (a)If the grating has 3,760 grooves per centimeter, what wavelength (in nm) describes each of these spectral lines? at ?1 = 12.8° ?A= nm ?1 = 14.2° ?B= nm ?1 = 15.0° ?C=. nm (b) At what angle (in degrees) would each of these lines be found in the second-order spectrum? for ?A ?2= ° for ?B ?2= ° for ?C ?2= °
Q1: If the refractive indexes of the mica plate in the direction of the slow axis and the fast axis are as follows: n =1.5977, n1= 1.5936, Find the thickness of this plate needed to make the optical path difference between the two rays passing through the plate equal to a quarter of the wavelength if light of its wavelength was passed through A = 5890 nm.
3. Calculate the polarization loss factor (PLF)...in db and dimensionless of an antenna whose electric field polarization is expressed as: E = (ax+ ay)E(r,0,0), when the electric field of the incident wave given by E, = ax E, (x, y)e-k=