Chapter #21 Solutions - Introduction to Optics - Leno M Pedrotti, Leno S Pedrotti, Frank L Pedrotti - 3rd Edition

 

1. a. Calculate the distances from the axis of the first three bright spots produced by a Ronchi ruling with transmitting slits of width 0.25 mm, as in Figure 21-2. Assume laser irradiation of 632.8 nm and a 50-cm focal length lens.b. What is the wavelength corresponding to the fundamental frequency?c. Determine the three lowest angular spatial frequencies, apart from the DC component, required in a Fourier representation of the Ronchi aperture function.d. What are the ratios of irradiance of the first three spots, relative to the irradiance of the “fundamental”? Get solution

2. a. When two transmission functions are put together, by physically placing two transparencies back-to-back in the aperture plane, how must the combined transmission function relate to the individual transmission functions?b. Consider an aperture function formed by two perpendicularly crossed Ronchi rulings. What would you expect to see in the spectrum plane? Get solution

3. The optical density of film is defined as the common logarithm of its opacity. The opacity, in turn, is just the reciprocal of the transmittance, T.a. Thus, show that optical density is equal to −log10 T.b. Show that the total optical density of several film layers is just the sum of their individual optical densities.c. What is the transmittance of five layers of film, each with an opacity of 1.25? What is the net optical density of the combined layers? Get solution

4. The sinusoidal transmission of a grating varies as 5 sin(ay), in arbitrary units.a. To produce faithfully the sinusoidal variation in the transmittance of the grating, what bias is required in the transmission function, assuming 100% maximum transmission?b. Sketch the aperture function with and without the bias term.c. What is the irradiance function at the detector for unit irradiance incident at the grating? Get solution

5. Prove the convolution theorem, that is, prove that if h(x)= f(x) ⊗ g(x)then ... Get solution

6. Plot the convolution in one dimension of two identical square pulses, of unit height and of 6 units length. Get solution

7. Determine the one-dimensional autocorrelation function Φ11(τ) for the sinusoidal function y = A sin (ωt + α). Get solution

8. a. The output of a Michelson spectrometer is fed to a photodetector. The input is mercury green light of 546.1 nm. If one mirror translates at a speed of 5 mm/s, what is the frequency of modulation of the photocurrent?b. What is the beat frequency of the photocurrent when the input is the yellow light of sodium, at 5889.95 Å, and 5895.92 Å? [Hint: Recall Eq. (8-14).] Get solution

9. The mirror translation in a Michelson spectrometer is 5 cm. What is the minimum resolvable wavelength at (a) 632.8 nm and at (b) 1 μm? Get solution

10. Light from a mercury lamp falls on the beam splitter of a student Michelson spectrometer. Wavelengths shorter than 360 nm are filtered from the light. The mirror translation rate is 71.5 nm/s. The rate at which spectrogram data is sampled is 1.28 readings/s. A total of 256 data points is fed to the computer for Fourier-trans form analysis. Find the (a) window width xω; (b) minimum resolvable wavelength interval at 400 nm; (c) minimum wavelength that is not subject to aliasing; (d) minimum sampling rale according to the Nyquist criterion. Get solution

11. The total path difference executed by a Fourier-transform spectrometer operating in the infrared is 2.78 mm. Its range is from 4400 to 400 cm−1.a. What is its resolution in wave number?b. How many data points must be taken over the scan to avoid aliasing within this range?c. What is the scan rate if one run is completed in 30 s? Get solution


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