When white light is normally occurrence on a diffraction grating the first order maximum for which colour of light occurs at the greatest angle with respect to the straight ahead direction?

Answer:

The length of the path that light should travel to get to a point on the screen from one slit in the diffraction grating must differ by one wavelength from the distance that light must travel to the same point from an adjacent slit in order to get maximal constructive interference. The greater the wavelength tends to the bigger the path difference needed. Additional from plane geometry the bigger the angle the bigger the path difference. Therefore we get first order interference at the biggest angle for the light with the longest wavelength. Red light has the longest observable light wavelength. Therefore red light yields the biggest angle for the first interference maximum.

We are able to as well get at this mathematically using the equation for the angles relative to the straight ahead direction of the interference maxima. The equation reads like

ml = d sinq

For first order interfering m=1 and the equation become

l = d sinq

Note that for a given diffraction harsh with a given slit separation d the greater the wavelength the greater the sinθ. Now intrusion maxima occur at angles between 0 and 90 degrees to either side of the straight-ahead direction. In that variety of angles the bigger the sinθ the bigger the angle θ itself. With red being the observable light having the longest wavelength

λ

,as well as with the longest wavelength interference maximum occurring at the biggest sinθ which in turn corresponds to the biggest θ we have a red light interference maximum occurring at the biggest angle of interference relative to the straight-ahead direction.