Reflection Grating

Reflection grating consists of an array of $N$ equally spaced, identical narrow reflecting grooves or ridges on a non-reflecting surface. The spacing between the grooves is $d=10^{-6}$ m. Light from a distant source falls normally (that is, perpendicularly to the surface) on the grating. A distant observer observes light reflected at angle $\theta$, see Fig. 2.

(a)

If the source emits blue light (wavelength $\lambda=450$ nm), what values of the angle $\theta$ correspond to principal maxima? Does the answer depend on $N$?

(b)

If the source emits red light (wavelength $\lambda=700$ nm), what values of $\theta$ correspond to principal maxima?

(c)

Using the above results, explain why the surface of a compact disc looks ``rainbow-colored'' when seen from an angle.

HINT: Natural light is a mixture of waves with wavelength spanning the whole spectrum from blue to red.

Figure: Reflection grating.