the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is…

the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°. the light forms a second - order bright band. how large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm

the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°. the light forms a second - order bright band. how large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm

Answer

Explanation:

Step1: Recall the formula for diffraction grating

The formula for the bright - fringes in a diffraction grating is $d\sin\theta = m\lambda$, where $d$ is the distance between slits, $\theta$ is the angle of diffraction, $m$ is the order of the bright - band, and $\lambda$ is the wavelength of light. The path - difference $\Delta x$ for a diffraction grating is given by $m\lambda$. So, $\Delta x=d\sin\theta$.

Step2: Convert the units

First, convert the distance between slits $d = 0.60\ mm=0.60\times10^{-3}\ m$ and the angle $\theta = 0.30^{\circ}$. The order $m = 2$.

Step3: Calculate the path - difference

Substitute the values into the formula $\Delta x=d\sin\theta$. $\Delta x=(0.60\times 10^{-3}\ m)\times\sin(0.30^{\circ})$ Since $\sin(0.30^{\circ})\approx0.005236$, then $\Delta x=(0.60\times 10^{-3}\ m)\times0.005236 = 3.1416\times10^{-6}\ m$. Convert to nanometers: $1\ m = 10^{9}\ nm$, so $\Delta x=3141.6\ nm\approx3142\ nm$.

Answer:

3142 nm