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

Answer:

1315789.47368 lines/m

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

$d=\dfrac{m\lambda}{sin\theta}\\\Rightarrow d=\dfrac{1\times 760}{1}\\\Rightarrow d=760\ nm$

The number of lines is the reciprocal of the slit distance

$n=\dfrac{1}{d}\\\Rightarrow n=\dfrac{1}{760\times 10^{-9}}\\\Rightarrow n=1315789.47368\ /m$

The number of lines is 1315789.47368 per meter