When hydrogen gas is excited (using electricity, for example), the hydrogen will emit light. One of the wavelengths from hydrogen is λ

λ=656 nm, which is called the hydrogen alpha line. Suppose the light from hydrogen gas is directed through a diffraction grating and the hydrogen alpha line produces a spectrum where the third maximum is θ.

θ=36 degrees away from the central maximum. You use a ruler to measure the width of the grating and find that it is w

w=2.6 cm. Calculate the number of lines in the grating.

This is a slit experiment type question. use the definitions of double slit experiments dsin(θ)=mλ/N

Question: Derive an algebraic expression for the number of lines in the grating. Type c to represent θ. Type ???? to represent λ.

N =

Hints:  The bright fringes from a grating are narrower than from a two-slit experiment. The equation for maxima is the same for two slits, three slits, and many slits.