light with a wavelength of about 490 nm is made to pass through a diffraction grating. the angle formed…

light with a wavelength of about 490 nm is made to pass through a diffraction grating. the angle formed between the path of the incident light and the diffracted light is 9.2° and forms a first - order bright band. what is the number of lines per mm in the diffraction grating? round your answer to the nearest whole number. lines per mm

light with a wavelength of about 490 nm is made to pass through a diffraction grating. the angle formed between the path of the incident light and the diffracted light is 9.2° and forms a first - order bright band. what is the number of lines per mm in the diffraction grating? round your answer to the nearest whole number. lines per mm

Answer

Explanation:

Step1: Recall the diffraction - grating formula

The formula for the diffraction grating is $d\sin\theta = m\lambda$, where $d$ is the distance between the slits, $\theta$ is the angle of diffraction, $m$ is the order of the bright - band, and $\lambda$ is the wavelength of the light. Here, $m = 1$, $\lambda=490\ nm = 490\times10^{-9}\ m$, and $\theta = 9.2^{\circ}$.

Step2: Solve for $d$

We can rewrite the formula as $d=\frac{m\lambda}{\sin\theta}$. Substituting the values, we have $d=\frac{1\times490\times 10^{-9}}{\sin(9.2^{\circ})}$. Since $\sin(9.2^{\circ})\approx0.16$, then $d=\frac{490\times 10^{-9}}{0.16}=3.0625\times 10^{-6}\ m$.

Step3: Convert $d$ to $mm$ and find the number of lines per $mm$

First, convert $d$ to $mm$: $d = 3.0625\times10^{-3}\ mm$. The number of lines per $mm$, $N=\frac{1}{d}$. So $N=\frac{1}{3.0625\times 10^{-3}}\approx327$ lines per $mm$.

Answer:

327