A diffraction grating $24\mathrm{.}0$ mm wide has $4500$ rulings. Light of wavelength $588$ nm is incident perpendicularly on the grating.

$($a$)$ What is the largest value of $$ at which a maximum appears on a distant viewing screen?

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$($b$)$ What is the second largest value of $$ at which a maximum appears on a distant viewing screen?

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$($c$)$ What is the third largest value of $$ at which a maximum appears on a distant viewing screen?

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