Explanation:
When rays of monochromatic light of wavelength \(\lambda\) are incident on a diffraction grating in which slit separation is \(d\), then for angle of diffraction \(\theta\), the following relation holds true.
\(\,\,\,\,\,\,\,\,\,\,\,d\sin \theta = n\lambda \)
where, \(n\) is called the spectrum order.
Given, \(n = 1,\lambda = 6500\mathop A\limits^ \circ \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6500 \times {10^{ - 10}}\;m\)
and \(\,\,\,\,\,\,\,\,\sin {30^ \circ } = \frac{1}{2}\)
\( \Rightarrow \,\,\,\,\,\,\,\,\,\,d = \frac{{n\lambda }}{{\sin {{30}^ \circ }}} = \frac{{6500 \times {{10}^{ - 10}}}}{{(1/2)}}\)
\( \Rightarrow \,\,\,\,\,\,\,\,\,d = 1.3 \times {10^{ - 6}}\;m\)