A diffraction grating produces a first-order maximum at an angle of 10 degree. What is the angle of the third order maximum?

For first order maxima, the angle Φ

Φ in radian = 1.5 λ / a

For third order maxima, the angle in radian

= 3.5 λ / a

Hence angle becomes 3.5/1.5 times in radian and therefore also in degree

Hence angle required is 10 x 3.5/1.5 degree or 23.33 degree.