Two diffraction gratings are located at the same distance from observation scree

Question

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?

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

Y = 1.22 L/d

thus d and Y are inverse to each other

hence is Y is more , d is less and vice versa

as such Grating B diffrats more

2. Y = mLR/d fro brigth fringe

3.Y = (m+0.5)LR/d fro dark fringe

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