Answer:
[tex]\theta_2 = 34.61^0[/tex]
Explanation:
Path difference for the destructive interference of a single slit:
[tex]D sin \theta = n \lambda[/tex]
For the first - order minimum, n = 1, and [tex]\theta = \theta_1[/tex]
[tex]D sin \theta_1 = \lambda[/tex].........(1)
For the second - order minimum, n = 2, and [tex]\theta = \theta_2[/tex]
[tex]D sin \theta_2 = 2 \lambda[/tex].........(2)
Dividing equation (2) by equation (1):
[tex]\frac{D sin \theta_2}{Dsin \theta_1} = \frac{2 \lambda}{\lambda} \\\frac{ sin \theta_2}{sin \theta_1} = 2 \\\theta_1 = 16.5^0\\\frac{ sin \theta_2}{sin 16.5} = 2\\sin \theta_2 = 2 sin 16.5\\sin \theta_2 = 0.568\\\theta_2 = sin^{-1} 0.568\\\theta_2 = 34.61^0[/tex]
