White light containing wavelengths from 410 nm to 750 nm falls on a grating with 7300 slits/cm. part a how wide is the first-order spectrum on a screen 3.60 m away?

Explanation:

Width of each slit d = 1 x 10⁻² / 7300

= 1.37 x 10⁻⁶ m

Distance of screen D = 3.6 m

for light of wavelength   λ   =  410 nm = 410 x 10⁻⁹ m

position of first maxima =λ D / d

= 410 x 10⁻⁹  x 3.6 / 1.37 x 10⁻⁶

= 1077.37 x 10⁻³ m

= 1.077 m

for light of wavelength   λ   =  750 nm = 750 x 10⁻⁹ m

position of first maxima =λ D / d

= 750 x 10⁻⁹  x 3.6 / 1.37 x 10⁻⁶

= 1438.54 x 10⁻³ m

= 1.438 m

width of first order spectrum = 1.438 - 1.077 m

= .361 m

36.1 cm .

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