Final answer:
The distance between two fringes produced by a diffraction grating can be calculated using the formula Ay = xλ/d. The distance between the two m=1 fringes is 1.7 cm.
Step-by-step explanation:
The distance between two fringes produced by a diffraction grating can be calculated using the formula Ay = xλ/d, where Ay is the distance between adjacent fringes, x is the distance of the viewing screen from the grating, λ is the wavelength of the light, and d is the spacing between the lines on the grating.
In this case, the grating has 620 lines per mm, which is equal to 62,000 lines per meter. The wavelength of the light is 520 nm, which is equal to 0.52 μm. The viewing screen is 2.1 m away.
Using the formula Ay = xλ/d, we can plug in the values to find the distance between the two m=1 fringes:
Ay = (2.1 m)(0.52 μm) / (62,000 lines/m) = 0.017 m = 1.7 cm
Therefore, the distance between the two m=1 fringes is 1.7 cm.