Diffraction Grating (a) Two diffraction gratings are located at the same distanc
ID: 2111718 • Letter: D
Question
Diffraction Grating(a) Two diffraction gratings are located at the same distance from observation screens. Light with same wavelength %u03BB is used for each. The principal maxima of grating A are observed to be closer together on the screen than the principal maxima of grating B. Which grating, if either, diffracts the light to a greater extent? Grating A diffracts light to a greater extent. Grating B diffracts light to a greater extent. The two gratings diffract the light to the same extent.
(b) Which grating, if either, has the smaller slit separation d? Grating A has the smaller slit separation d. Both gratings have the same slit separation. Grating B has the smaller slit separation d.
(c) Which grating, if either, has the greater number of lines per meter? Grating A has the greater number of lines per meter. The two gratings have the same number of lines per meter. Grating B has the greater number of lines per meter.
The separation between adjacent principal maxima for grating A is 1.7 cm, and for grating B it is 4.4cm. Grating A has 8000 lines per meter.
(d) What is the algebraic expression for the distance y of a principal maximum from the midpoint of the central bright fringe on the screen? Express your answer in terms of the angle %u03B8 that locates the principal maximum and the distance L between the grating and the screen.
y =
(e) Assume that the values for %u03B8 are small enough that tan %u03B8 %u2248 sin %u03B8. What is the algebraic expression for the distance y of a principal maximum from the midpoint of the central bright fringe on the screen? Express your answer in terms of the distance L between the grating and the screen, the wavelength %u03BB of the light, the separation d between the slits of the grating, and the integer variable m = 0, 1, 2, 3, ... .
y =
(f) Assume that the values for %u03B8 are small enough that tan %u03B8 %u2248 sin %u03B8. What is the algebraic expression for the separation %u0394y = ym + 1 - ym on the screen between adjacent principal maxima? Express your answer in terms of the distance L between the grating and the screen, the wavelength %u03BBof the light, and the separation d between the slits of the grating.
%u0394y = ym + 1 - ym =
(g) What is the algebraic expression for the separation %u0394y = ym + 1 - ym on the screen between adjacent principal maxima? Express your answer in terms of the distance L between the grating and the screen, the wavelength %u03BB of the light, and the number N of lines per meter that a grating has.
%u0394y = ym + 1 - ym =
(h) What is the algebraic expression for the number NB of lines per meter that grating B has? Express your answer in terms of the number NA of lines per meter that grating A has, the separation %u0394yAbetween adjacent principal maxima for grating A, and the separation %u0394yB between adjacent principal maxima for grating B.
NB =
(i) What is the number NB of lines per meter that grating B has?
NB = lines per meter
Explanation / Answer
Apply y/L - m(wavelength)/d Since m, L, and wavelength are the same for both, we can set up a proportion. d is the inverse of the lines per meter, so yd = yd (2.7)(1/2339) = (3.2)(d) d = 3.607 X 10^-4 Take the inverse of that and get 1/3.607 X 10^-4 = 2772 lines per meter