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Light of wavelength 600 nm illuminates a diffraction grating. the second-order maximum is at angle 39.5 ∘. part a how many lines per millimeter does this grating have?

Respuesta :

jushmk
Diffraction equation applies in this case:

d*Sin x = m*wavelength, where d = spacing of lines, x = angle = 39.5°, m = order of maximum = 2

Substituting;
d* Sin 39.5 = 2*600*10^-9
d = (2*600*10^-9)/Sin 39.5 = 1.88656*10^-6 m

In 1 mm (or 0.001 m), the number of lines is given as;
Number of lines = 0.001/d = 0.001/(1.88656*10^-6) = 530.065 ≈ 530 lines
batolisis

The number of lines per millimeter that the grating has is : ≈ 530 lines

Given data :

light wavelength = 600 nm

second order maximum angle ( x ) = 39.5°

order of maximum = 2

Determine the number of lines the grating will have

We will apply diffraction equation

[tex]d*sinx = m*wavelength[/tex] --- ( 1 )

where : d = spacing of lines, x =  39.5°, m = 2

Insert values into equation ( 1 ) above

d * Sin ( 39.5 ) = 2 * 600 * 10⁻⁹

therefore ; d = 1.88656 * 10⁻⁶ m

Final step : determine the number of lines per mm

Number of lines per mm

= 0.001 / d

= 0.001 / (1.88656 * 10⁻⁶ )  ≈ 530 lines

Hence we can conclude that The number of lines per millimeter that the grating has is ≈ 530 lines

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