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Textbook Guide Physics: Diffraction Grating, Small-Angle Approximation, Halfwidth And Fullwidth Forms

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grayraven524
1 Dec 2016
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Physics
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PHY131H1
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PHY131H1 Full Course Notes
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PHY131H1 Full Course Notes
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Document Summary

Chapter 36 diffraction: when waves encounter an edge, obstacle, or aperture the size of which is comparable to the wavelength of the waves, the waves diffract or spread out (diffraction pattern) as they travel and undergo interference. 36-2 intensity in single-slit diffraction: the intensity of the diffraction pattern of a single-slit diffraction at any given angle is given by: represents the intensity at the center of the pattern. 36-4 diffraction by a double slit: diffraction by two slits produce a combined double-slit interference and diffraction by each is expressed as the slits are the pattern identical, slit. 36-6 gratings: dispersion and resolving power: the spreading of waves and diffraction lines by wavelength created by diffraction gratings is referred to as dispersion most accurately, dispersion is the measure of the angular separation ( ) of the line it produces for the differing wavelengths (

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Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

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Related Questions

Two finite-width slits are illuminated by a parallel beam of lightof wavelength 635 nm. The resulting pattern is observed on a screenat a distance of 1.60m from the slits. The central brightdiffraction fringe has a width of 4.20 cm. It is observed that thefourth interference maximum on either side is missing.
(a) What is the width of each slit?
(b) What is the distance between the slits?
(c) What other interference maxima (if any) are missing?
(d) Sketch the intensity as a function of distance from the centerof the pattern.
(Your sketch should include three bright diffraction fringes, thecentral one and the first one on either side.)

A single slit with a width of 0.100 mm is illuminated by lightwitha wavelength 610 nm.
(a) What is the angular location of the firstdiffractionminimum?
? rad
(b) What is the angular location of the seconddiffractionminimum?
? rad
(c) Diffraction maxima occur approximately halfway betweenadjacentdiffraction minima. Using your results from (a) and (b),calculatethe approximate angular location of the first diffractionpeak tothe left or right of the central diffraction peak.
? rad
(d) To obtain the "exact" locations of diffraction maxima, valuesofalpha are required at which intensity maxima occur for asingleslit. An equation for these values of alpha are obtainedbydifferentiating Eq. 36-5 with respect to alpha and equatingtheresult to zero. Two equations are obtained: (1) The firstequation,sin / = 0, is the condition that must be satisfied whenthere is adiffraction minima. (2) The second equation of the form(sin )n1(cos )n2 = ()n3 is the condition that must be satisfiedwhen thereis a diffraction maxima. What are the values of theintegers n1, n2and n3, at least one of which is negative?
n1= ?
n2= ?
n3= ?
(e) It is not possible to exactly solve the equation fordiffractionmaxima to obtain a general formula for the location ofalldiffraction maxima; however, the values of alpha that satisfythisequation can be found graphically by plotting the curve y =(sin )n1(cos )n2 and the curve y = ()n3 and determining where thetwo curvesintersect. The smallest two values of alpha that satisfytheequation are alpha = 0 and alpha = 4.4934. The first solutionisexact, and the second and all others are only approximate. Usingthesolution alpha = 4.4934, solve for the angular location thetaof thediffraction peak adjacent to the central peak.
? rad
(f) Calculate the percent error between the actual value ofthetacalculated in (e) and the approximate value calculated in(c).
????%

I have a and b need help with the rest. This is a modifiedversionof Chap. 36 #15. Thanks

If a virtual image is formed 9.0 cm along the principal axis from aconvex mirror of focal length –15.0 cm, how far is the object fromthe mirror?

2. A woman looking in a makeup mirror sees her face at twice itsactual size and right-side up. If she is 26.0 cm from the mirror,what is its focal length?

3. Which of the following best describes the image of a concavemirror when the object is at a distance greater than twice thefocal point distance from the mirror?
a. virtual, upright and magnification greater than one
b. real, inverted and magnification less than one
c. virtual, upright and magnification less than one
d. real, inverted and magnification greater than one

4. A convex mirror with focal length of ?18 cm forms an image 12 cmbehind the surface. Where is the object located as measured fromthe surface?

5. A convex mirror with a focal length of ?18 cm forms an image 15cm behind the surface. If the object height is 1.2 cm what is theimage height?

6. An object placed 14 cm from a concave mirror produces a realimage 8.0 cm from the mirror. If the object is now moved to a newposition 18.0 cm from the mirror, where is the new image located asmeasured from the mirror?

7. When the reflection of an object is seen in a concave mirror theimage will:

8. A candle is 40.0 cm in front of a convex spherical mirror ofradius of curvature 70.0 cm. What are the image distance and themagnification, respectively?

9. An object is 16.0 cm from the surface of a spherical Christmastree ornament that is 8.00 cm in diameter. What is themagnification of the image?

10. A solid glass sphere with a radius of 6.00 cm and index ofrefraction of 1.50 has a small coin embedded 3.00 cm from the frontsurface of the sphere. For the viewer looking at the coin throughthe glass, at what distance from the front surface of the glassdoes the coin’s image appear to be located?

11. A glass block, for which n = 1.52, has a blemish located 4.5 cmfrom one surface. At what distance from that surface does the imageof the blemish appear to the outside observer?

12. An object of length 2.00 cm is inside a plastic block withindex of refraction 1.50. If the object is viewed from directlyabove, what is the length of its image?

13. An object is placed at a distance of 25 cm from a thin convexlens along its axis. The lens has a focal length of 10 cm. What arethe values, respectively, of the image distance andmagnification?
14. An object is placed at a distance of 50 cm from a thin lensalong the axis. If a real image forms at a distance of 35 cm fromthe lens, on the opposite side from the object, what is the focallength of the lens?

15. A contact lens is made of plastic with an index of refraction1.50. The lens has an outer radius of curvature of +2.0 cm and aninner radius of curvature of +2.5 cm. What is its focallength?

16. A Young’s double slit has a slit separation of 2.50 ? 10?5 m onwhich a monochromatic light beam is directed. The resultant brightfringes on a screen 2.00 m from the double slit are separated by2.30 ? 10?2 m. What is the wavelength of this beam? (1 nm = 10?9m)

17. A Young’s double-slit apparatus is set up so that a screen ispositioned 1.9 m from the double slits, and the spacing between thetwo slits is 0.040 mm. What is the distance between alternatingbright fringes on the screen if the light source has a wavelengthof 630 nm? (1 nm = 10?9 m)

18. The blue tint of a coated camera lens is largely caused by whateffects?

19. What is the minimum thickness of a glycerin film (n = 1.47) onwhich light of wavelength 650 nm shines that results inconstructive interference of the reflected light? Assume the filmis surrounded front and back by air.

20. Light of wavelength 560 nm is incident on a slit of width 0.150mm, and a diffraction pattern is produced on a screen that is 2.00m from the slit. What is the width of the central bright fringe? (1nm = 10?9 m)

21. Light of wavelength 610 nm is incident on a slit of width 0.25mm, and a diffraction pattern is produced on a screen that is 1.5 mfrom the slit. What is the distance of the second dark fringe fromthe center of the bright fringe? (1 nm = 10?9 m)

22. A multiple slit diffraction grating has a slit separation of2.50 ? 10?6 m. Find the wavelength of the monochromatic light thatwill have its second order bright fringe diffracted through anangle of 38.0°. (1 nm = 10?9 m)

23. A diffraction grating with 12 000 lines/cm will exhibit thefirst order maximum for light of wavelength 510 nm at what angle?(1 nm = 10?9 m)

24. A beam of unpolarized light in air strikes a flat piece ofglass at an angle of incidence of 58.0°. If the reflected beam iscompletely polarized, what is the index of refraction of theglass?

25. A beam of polarized light of intensity I0 passes through asheet of ideal polarizing material. The polarization axis of thebeam and the transmission axis of the sheet differ by 45°. What isthe intensity of the emerging light?

26. At what angle is the sun above the horizon if its light isfound to be completely polarized when it is reflected from the topsurface of a slab of glass (n = 1.65)?