Question

What is the maximum number of lines per centimeter a diffraction grating can have and produce a complete first-order spectrum for visible light? (Assume that the range of visible wavelengths of light in air is 380 - 760 nm.)

Answer 1

1315789.47368 lines/m

Step-by-step explanation:

m = Order = 1

`sin\theta` = 1 For maximum condition

`\lambda` = Wavelength = 760 nm maximum

From Rayleigh criteria we have the expression for the gap

`d=(m\lambda)/(sin\theta)\\\Rightarrow d=(1* 760)/(1)\\\Rightarrow d=760\ nm`

The number of lines is the reciprocal of the slit distance

`n=(1)/(d)\\\Rightarrow n=(1)/(760* 10^(-9))\\\Rightarrow n=1315789.47368\ /m`

The number of lines is 1315789.47368 per meter