Calculate the difference of the angles (in degrees) of second and first diffract

Question

Calculate the difference of the angles (in degrees) of second and first diffraction maxima for light with lambda = 481 nm and diffraction grating d = 14, 911 lines/inch (1 inch = 2.54 cm). Express the answer to one decimal place. What is the angular separation in degrees of two spectral lines of wavelengths 436 nm and 354 nm formed in order m = 2 with a 360 line/mm grating? Express the answer (numerical value only) with two decimal places. What is the correct relation for the wavelengths of red, blue and green spectral lines? lambda_R

Explanation / Answer

condition for diffraction maximuma is

a sin theta = m lamda

d= 14911 lines/ in

a= 1/d = 1/14911 lines/ in =6.70* 10^-5 inch = 6.70 * 10^-5 ( 0.0254) = 1.70 * 10^-6

theta1 = sin^-1 ( m lamda/ a)

= sin^-1 ( 1 ( 481 * 10^-9)/ 1.70 * 10^-6)

=16.43

theta2 = sin^-1 ( m lamda/ a)

= sin^-1 ( 2 ( 481 * 10^-9)/ 1.70 * 10^-6)

=34.46

difference = 34.46 - 16.43 = 18 degree

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d= 1/N = 1/360 lines/ mm = 2.77 * 10^-6 m

theta = sin^-1 ( m lamda/ d)

= sin^-1 ( 2 ( 436 * 10^-9)/ 2.77 * 10^-6 m)

=18.34

theta = sin^-1 ( m lamda/ d)

= sin^-1 ( 2 ( 354 * 10^-9)/ 2.77 * 10^-6 m)

=14.8

difference = 18.34-14.8 = 3.53 degree

as per guide lines I worked first two question kindly post remaining questions in the next post

  

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