Light of wavelength 545 nm passes through a diffraction grating with 1.35 x103 s

Question

Light of wavelength 545 nm passes through a diffraction grating with 1.35 x103 slits/cm. The diffraction pattern is observed on a screen 1.70 cm from the grating. a) Determine the separation distance between the adjacent maxima on the screen. b) A second monochromatic light illuminates the diffraction grating simultaneously. The 2. second-order maximum of the second light falls midway between the central maximum and the first-order maximum for the first light on the screen. Determine the wavelength of the second light.

Explanation / Answer

use Y = mLR/d

for m=1

d = 1/(1350*100) =

Y = 1 * 545*10^-9 * 0.017* 1350*100

Y = 1.25 mm

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for L2 = ?

Y2 = 1.5 Y

m = 2

so Y2 = mL2R/d

L2 = Y2 *d/mR

L2 = (1.5*1.25 *10^-3)* (1/1350*100)/(2*0.017)

L2 = 408 nm

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