In a diffraction 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?
A)479 nm
B)497 nm
C)567 nm
D)749 nm
E)794 nm

Question

Quizplus · Accepted Answer

The position of maxima in a diffraction pattern is given by $ y = \frac{m \lambda L}{d} $, where $ m $ is the order, $ \lambda $ is the wavelength, $ L $ is the distance to the screen, and $ d $ is the grating spacing. For the first source, $ y_1 = 0.350 $ mm, $ m_1 = 1 $, and $ \lambda_1 = 600 $ nm. For the second source, $ y_2 = 0.870 $ mm and $ m_2 = 3 $. Using the ratio $ \frac{y_2}{y_1} = \frac{m_2 \lambda_2}{m_1 \lambda_1} $, we find $ \lambda_2 = \frac{y_2 \cdot m_1 \cdot \lambda_1}{y_1 \cdot m_2} = \frac{0.870 \cdot 1 \cdot 600}{0.350 \cdot 3} = 497 $ nm.

In a Diffraction Experiment, Light of 600 Nm Wavelength Produces