yellow light (600 nm) passes through a diffraction grating with d = 2.35 x 10-6 m. what is the angular…

Explanation:

Step1: Recall the diffraction - grating formula

The formula for the maxima in a diffraction grating is $d\sin\theta = m\lambda$, where $d$ is the slit - separation, $\theta$ is the angular position of the maximum, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. First, convert the wavelength to SI units: $\lambda=600\ nm = 600\times10^{-9}\ m$ and $d = 2.35\times10^{-6}\ m$.

Step2: Find the angle for $m = 2$

From $d\sin\theta_2=m_2\lambda$, we can solve for $\theta_2$. $\sin\theta_2=\frac{m_2\lambda}{d}=\frac{2\times600\times 10^{-9}}{2.35\times10^{-6}}=\frac{1200\times10^{-9}}{2.35\times10^{-6}}=\frac{1200}{2.35\times10^{3}}\approx0.5106$ $\theta_2=\sin^{-1}(0.5106)\approx30.7^{\circ}$

Step3: Find the angle for $m = 3$

From $d\sin\theta_3=m_3\lambda$, we can solve for $\theta_3$. $\sin\theta_3=\frac{m_3\lambda}{d}=\frac{3\times600\times 10^{-9}}{2.35\times10^{-6}}=\frac{1800\times10^{-9}}{2.35\times10^{-6}}=\frac{1800}{2.35\times10^{3}}\approx0.766$ $\theta_3=\sin^{-1}(0.766)\approx49.9^{\circ}$

Step4: Calculate the angular separation

The angular separation $\Delta\theta=\theta_3 - \theta_2$. $\Delta\theta=49.9^{\circ}-30.7^{\circ}=19.2^{\circ}$

Answer:

$19.2$