Question:

Light from a laser is directed normally at a diffracted grating, as illustrated in the figure below.

The diffraction grating is situated at the center of a circular scale, marked in degrees. The readings on the scale for the second order diffracted beams are $\displaystyle 136^o$ and $\displaystyle 162^o$.

The wavelength of the laser light is $\displaystyle 630nm$.

Calculate the spacing of the slits of the diffraction grating.

Attempt:

$\displaystyle

d\sin\theta = \lambda{n}$

$\displaystyle

\theta = \frac{1}{2}(162 - 136) = 13^o$

$\displaystyle d\sin{13} = {\color{red}2} \times 630 \times 10^{-9}$

$\displaystyle n = 2$ because there are I took 2 reading? or is there another reason?