A diffraction grating has 5000 lines per centimeter and is 1.5 centimeters wide.When radiation is incident upon the grating a second-order maximum is observed at an angle of 37º.The wavelength of this light is
A)400 nm
B)600 nm
C)900 nm
D)1200 nm
E)2400 nm

Question

Quizplus · Accepted Answer

The wavelength ($\lambda$) can be found using the grating equation $d\sin(\theta) = m\lambda$, where $d$ is the grating spacing, $\theta$ is the diffraction angle, and $m$ is the order of the maximum. Given 5000 lines per cm, the spacing $d = \frac{1}{5000 \text{ lines/cm}} = \frac{1}{500000 \text{ lines/m}} = 2 \times 10^{-6} \text{ m}$. For the second-order maximum ($m = 2$) at $37^\circ$, solving for $\lambda$ gives $\lambda = \frac{d\sin(\theta)}{m} = \frac{2 \times 10^{-6} \text{ m} \times \sin(37^\circ)}{2} \approx 600 \text{ nm}$.

A Diffraction Grating Has 5000 Lines Per Centimeter and Is