Question

A diffraction grating gives a second-order maximum at as angle of 31° for violet light (λ = 4.0 × 102 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating? [___/3]

Answer 1

for second order maximum we can say

$a sin\theta = \frac{5\lambda}{2}$

here we will have

$a= \frac{0.01}{N}$

now we will have

$\frac{0.01}{N} sin31 = \frac{5*400*10^{-9}}{2}$

$N = \frac{0.01 * sin31}{5*200*10^{-9}}$

$N = 5150$

so the number of lines are 5150.