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

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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 millime

Question

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?

## Answers ( 2 )

The

number of linesper millimeter that thegratinghas is:u2248530 linesGiven data :light wavelength = 600 nm

second order maximum angle ( x ) = 39.5u00b0

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 = 39.5u00b0, m = 2

Insert values into

equation ( 1 )aboved * Sin ( 39.5 ) = 2 * 600 * 10u207bu2079

therefore ;

d = 1.88656 * 10u207bu2076 mFinal step : determine the number of lines per mmNumber of linesper mm= 0.001 / d

= 0.001 / (1.88656 * 10u207bu2076 ) u2248

530 linesHence we can conclude that Theu2248

number of linesper millimeter that thegratinghas is530 linesLearn more about

grating: https://brainly.com/question/25804706Diffraction equation applies in this case:

d*Sin x = m*wavelength, where d = spacing of lines, x = angle = 39.5u00b0, 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) = 530.065u2248 530 lines