Monochromatic light is incident on a diffraction grating that is 75 mm wide and ruled with 50,000 lines.The second-order maximum is seen at 32.5°.What is the wavelength of the incident light?
A)202 nm
B)403 nm
C)605 nm
D)806 nm

Question

Quizplus · Accepted Answer

The wavelength ($\lambda$) can be calculated using the diffraction 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 that the grating is 75 mm wide with 50,000 lines, the spacing $d = \frac{75 mm}{50,000} = 1.5 \times 10^{-3} mm = 1.5 \times 10^{-6} m$. For the second-order maximum ($m = 2$) at $\theta = 32.5°$, solving for $\lambda$ gives $\lambda = \frac{d\sin\theta}{m} = \frac{1.5 \times 10^{-6} \sin(32.5°)}{2} \approx 403 nm$.

Monochromatic Light Is Incident on a Diffraction Grating That Is