Problem 5: A laser beam with wavelength 2 475 nm hits a grating with n = 2250 gr

Question

Problem 5: A laser beam with wavelength 2 475 nm hits a grating with n = 2250 grooves per centimeter. Randomized Variables Part (a) Express the grating spacing, d, in terms of n. Expression : _ Select from the variables below to write your expression. Note that all variables may not be required. Part (b) Calculate the numerical value of d in cm Numeric : A numeric value is expected and not an expression. Part (t) Find the sin of the angle, theta 2, at which the 2nd order maximum will be observed, in terms of d and Select from the variables below to write your expression Note that all variables may not be require& a, ?, lambda, theta, a, d, g, h, i, j, k m, n, P, t Part (d) Calculate the numerical value of 82 in degrees. Numeric : A numeric value is expected and not an expression.

Explanation / Answer

In interfreence or diffraction pattern,

the needed equation is Y = mLR/d---------------1

and d sin theta = mL--------------------2

where L = wavelgnth,

m = order = 1,2,3,4, ......... for brigth bands

m = 1.5, 2.5, 3.5, 4.5, ......for dark bands

R is the distance from slit to screen,

Y = disatnce from central spot to nth order fringe

so

a. d sin theta    = mL

so

so d = 1 * 402 e-9/(sin 3)

d = 7.681 um
-----------------

b. No. of lines N = 1/d = 1/7.681e-

N = 130191 lines per m
-----------------------

c.

d sin theta = mL

sin theta = 2* 402 e-9/7.681 e-6

sin theta = 0.1046

theta =   6 deg

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