Answer:
1 bright fringe every 33 cm.
Explanation:
The formula to calculate the position of the m-th order brigh line (constructive interference) produced by diffraction of light through a diffraction grating is:
![y=\frac{m\lambda D}{d}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bm%5Clambda%20D%7D%7Bd%7D)
where
m is the order of the maximum
is the wavelength of the light
D is the distance of the screen
d is the separation between two adjacent slit
Here we have:
is the wavelength of the light
D = 1 m is the distance of the screen (not given in the problem, so we assume it to be 1 meter)
is the number of lines per mm, so the spacing between two lines is
![d=\frac{1}{n}=\frac{1}{520}=1.92\cdot 10^{-3} mm = 1.92\cdot 10^{-6} m](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B1%7D%7Bn%7D%3D%5Cfrac%7B1%7D%7B520%7D%3D1.92%5Ccdot%2010%5E%7B-3%7D%20mm%20%3D%201.92%5Ccdot%2010%5E%7B-6%7D%20m)
Therefore, substituting m = 1, we find:
![y=\frac{(632.8\cdot 10^{-9})(1)}{1.92\cdot 10^{-6}}=0.330 m](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%28632.8%5Ccdot%2010%5E%7B-9%7D%29%281%29%7D%7B1.92%5Ccdot%2010%5E%7B-6%7D%7D%3D0.330%20m)
So, on the distant screen, there is 1 bright fringe every 33 cm.