Question

Red light of wavelength $625\, nm$ is incident normally on an optical diffraction grating with $2 \times 10^5\, lines/m$. Including central principal maxima, how many maxima may be observed on a screen which is far from the grating?

• A. $15$
• B. $17$
• C. $20$
• D. $18$

Answer 1

Answer: (B)

For principle maxima in grating spectra
$\frac{\sin \theta}{N}=n \lambda$
where, $n=(1,2,3)$ is the order of principle maximum and $\theta$ is the angle of diffraction.
$n=\frac{1}{\lambda N}=\frac{1}{6.25 \times 10^{-7} \times 2 \times 10^{5}}=8$
$\therefore $ Number of maxima $=2 n+ 1=2 \times 8+1=17$