In a diffraction grating experiment, light of 600 nm wavelength produces a first-order maximum 0.350 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum 0.870 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source

∧2 = 497 nm

Explanation:

d = the spacing between every two lines

D = the distance from the grating to the screen

∧1 = wavelength from the fist source

∧2 = wavelength from the second source

The first order maximum y1 = 0.350 mm

The third order maximum y2 = 0.870 mm

∧1 = 600 nm

∧2 = ?

Therefore,

1 × ∧1 = d × y1 / D  

3 × ∧2 = d × y2 / D

divide the ∧2 by ∧1

3∧2/∧1 = y2/y1

∧2 = (y2 × ∧1 )/ 3 × y1

∧2 = (0.870 × 600) / 3 × 0.350

∧2 = 522/1.05

∧2 = 497.142857143

∧2 = 497 nm

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