A beam of light that consists of a mixture of red light ($\lambda$ = 660 nm in vacuum) and violet light ($\lambda$ = 410 nm in vacuum) falls on a grating that contains 1.0 × 10⁴ lines/cm. Find the angular separation between the first-order maxima of the two wavelengths if the experiment takes place in a vacuum. A)11° B)17° C)24° D)41° E)65°

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Quizplus · Accepted Answer

The angular separation between the first-order maxima can be found using the grating equation $d \sin \theta = m \lambda$, where $d$ is the distance between the lines on the grating, $\theta$ is the angle, $m$ is the order of the maximum, and $\lambda$ is the wavelength. For the first-order maxima ($m=1$), calculate $\theta$ for both wavelengths and find the difference. The grating spacing $d = 1/(1.0 \times 10^4 \text{ lines/cm}) = 1 \times 10^{-6} \text{ m}$. For red light, $\theta_r = \arcsin((660 \times 10^{-9})/(1 \times 10^{-6}))$, and for violet light, $\theta_v = \arcsin((410 \times 10^{-9})/(1 \times 10^{-6}))$. The angular separation is $\theta_r - \theta_v \approx 17^\circ$.

A Beam of Light That Consists of a Mixture of Red