Chapter #13 Solutions - Introduction to Optics - Leno M Pedrotti, Leno S Pedrotti, Frank L Pedrotti - 3rd Edition

 

1. A 1-mm-diameter hole is illuminated by plane waves of 546-nm light. According to the usual criterion, which technique (near-field or far-field) may be applied to the diffraction problem when the detector is at 50 cm, 1 m, and 5 m from the aperture? Get solution

2. A 3-mm-diameter circular hole in an opaque screen is illuminated normally by plane waves of wavelength 550 nm. A small photocell is moved along the central axis, recording the power density of the diffracted beam. Determine the locations of the first three maxima and minima as the photocell approaches the screen.Figure 1.... Get solution

3. A distant source of sodium light (589.3 nm) illuminates a circular hole. As the hole increases in diameter, the irradiance at an axial point 1.5 m from the hole passes alternately through maxima and minima. What are the diameters of the holes that produce (a) the first two maxima and (b) the first two minima? Get solution

4. Plane waves of monochromatic (600-nm) light are incident on an aperture. A detector is situated on axis at a distance of 20 cm from the aperture plane.a. What is the value of R1, the radius of the first Fresnel half-period zone, relative to the detector?b. If the aperture is a circle of radius 1 cm, centered on axis, how many half-period zones does it contain?c. If the aperture is a zone plate with every other zone blocked out and with the radius of the first zone equal to R1 (found in (a)), determine the first three focal lengths of the zone plate. Get solution

5. The zone plate radii given by Eq. (13-20) were derived for the case of plane waves incident on the aperture. If instead the incident waves are spherical, from an axial point source at distance p from the aperture, show that the necessary modification yields ...where q is the distance from aperture to the axial point of detection and L is defined by 1/L = 1/p + 1/q.Figure 1.... Get solution

6. Repeal parts (a) and (b) of problem 1 when the source is a point source 10 cm from the aperture. Take into account the results of problem 2.Problem 1–21. Plane waves of monochromatic (600-nm) light are incident on an aperture. A detector is situated on axis at a distance of 20 cm from the aperture plane.a. What is the value of R1, the radius of the first Fresnel half-period zone, relative to the detector?b. If the aperture is a circle of radius 1 cm, centered on axis, how many half-period zones does it contain?c. If the aperture is a zone plate with every other zone blocked out and with the radius of the first zone equal to R1 (found in (a)), determine the first three focal lengths of the zone plate.2. The zone plate radii given by Eq. (13-20) were derived for the case of plane waves incident on the aperture. If instead the incident waves are spherical, from an axial point source at distance p from the aperture, show that the necessary modification yields ...where q is the distance from aperture to the axial point of detection and L is defined by 1/L = 1/p + 1/q.Figure 1.... Get solution

7. A point source of monochromatic light (500 nm) is 50 cm from an aperture plane. The detection point is located 50 cm on the other side of the aperture plane.a. The transmitting portion of the aperture plane is an annular ring of inner radius 0.500 mm and outer radius 0.935 mm. What is the irradiance at the detector relative to the irradiance there for an unobstructed wavefront? The results of problem 1 will be helpful.b. Answer the same question if the outer radius is 1.00 mm.c. How many half-period zones are included in the annular ring in each case?Problem 1The zone plate radii given by Eq. (13-20) were derived for the case of plane waves incident on the aperture. If instead the incident waves are spherical, from an axial point source at distance p from the aperture, show that the necessary modification yields ...where q is the distance from aperture to the axial point of detection and L is defined by 1/L = 1/p + 1/q.Figure 1.... Get solution

8. By what percentage does the area of the 25th Fresnel half-period zone differ from that of the first, for the case when source and detector are both 50 cm from the aperture and the source supplies light at 500 nm? Get solution

9. A zone plate is to be produced having a focal length of 2 m for a He-Ne laser of wavelength 632.8 nm. An ink drawing of 20 zones is made with alternate zones shaded in, and a reduced photographic transparency is made of the drawing.a. If the radius of the first zone is 11.25 cm in the drawing, what reduction factor is required?b. What is the radius of the last zone in the drawing? Get solution

10. A zone plate has its center half-zone opaque. Find the diameters of the first three clear zones such that the plate focuses parallel light of wavelength 550 nm at 25 cm from the plate.Figure 1.... Get solution

11. For an incident plane wavefront, show that the areas of the Fresnel half-period zones relative to an observation point at distance x from the wavefront are approximately constant and equal to πλx. Assume that λ/x is much smaller than 1. Get solution

12. Light of wavelength 485 nm is incident normally on a screen. How large is a circular opening in an otherwise opaque screen if it transmits four Fresnel zones to a point 2 m away? What, approximately, is the irradiance at the point? Get solution

13. A single slit of width ... millimeter is illuminated by a collimated beam of light of wavelength 540 nm. At what observation point on the axis does Δv = 2.5? Get solution

14. A source slit at one end of an optical bench is illuminated by monochromatic mercury light of 435.8 nm. The beam diverging from the source slit encounters a second slit 0.5 mm wide at a distance of 30 cm. The diffracted light is observed on a screen at 15 cm farther along the optical bench. Determine the irradiance (in terms of the unobstructed irradiance) at the screen (a) on axis and (b) at one edge of the geometrical shadow of the diffracting slit.Figure 1.... Get solution

16. Filtered green mercury light (546.1 nm) emerges from a slit placed 30 cm from a rod 1.5 mm thick. The diffraction pattern formed by the rod is examined in a plane at 60 cm beyond the rod. Calculate the irradiance of the pattern at (a) the center of the geometrical shadow of the rod and (b) the edge of the geometrical shadow. Get solution

17. For the near-field diffraction pattern of a straight edge, calculate the irradiance of the second maximum and minimum, using the Cornu spiral and the table of Fresnel integral values given. Get solution

19. Calculate the relative irradiance (compared to the unobstructed irradiance) on the optic axis due to a double-slit aperture that is both 10 cm from a point source of monochromatic light (546 nm) and 10 cm from the observation screen. The slits are 0.04 mm in width and separated (center to center) by 0.25 mm.Figure 1... Get solution

20. Single-slit diffraction is produced using a monochromatic light source (435.8 nm) at 25 cm from the slit. The slit is 0.75 mm wide. A detector is placed on the axis, 25 cm from the slit.a. Ensure that far-field diffraction is invalid in this case.b. Nevertheless, determine the distance above the axis at which single-slit Fraunhofer diffraction predicts the first zero in irradiance.c. Then calculate the irradiance at the same point, using Fresnel diffraction and the Cornu spiral. Express the result in terms of the unobstructed irradiance. Get solution

21. A glass plate is sprayed with uniform opaque particles. When a distant point source of light is observed looking through the plate, a diffuse halo is seen whose angular width is about 2°. Estimate the size of the particles. (Hint: Use Babinet’s principle.) Get solution


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