A diffraction grating is made up of slits of width 300 nm...

A diffraction grating is made up of slits of width 300 nm with separation 900 $\mathrm{nm}$ . The grating is illuminated by monochromatic plane waves of wavelength $\lambda=600 \mathrm{nm}$ at normal incidence. (a) How many maxima are there in the full diffraction pattern? (b) What is the angular width of a spectral line observed in the first order if the grating has 1000 slits?

A diffraction grating is made up of slits of width 300 nm with separation 900 $\mathrm{nm}$ . The grating is illuminated by monochromatic
plane waves of wavelength $\lambda=600 \mathrm{nm}$ at normal incidence.
(a) How many maxima are there in the full diffraction pattern?
(b) What is the angular width of a spectral line observed in the first
order if the grating has 1000 slits?

Key Concepts

Finite Slit Width and Diffraction Envelope

Each slit in a grating has a finite width, which means that the light diffracted from an individual slit forms its own intensity pattern, often called the diffraction envelope. This envelope modulates the sharper interference maxima produced by the multiple slits. The position of zeros in the single-slit diffraction pattern can suppress certain interference maxima if they coincide.

Angular Width of Diffraction Maximum

When a diffraction grating has a finite number of slits, the principal interference maximum is not an infinitely narrow spike but has a finite angular width. This angular width, which affects the resolving power of the grating, is inversely related to the total number of slits and the overall grating size. It is typically estimated using the relation ?? ? ?/(Nd cos?) for small angles, where N is the number of slits and d is the slit separation.

Diffraction Grating

A diffraction grating is an optical component with a regular pattern (typically many parallel slits) that splits and diffracts light into several beams traveling in different directions. The directions of these beams depend on the spacing between the slits and the wavelength of the light, and are governed by the principle of interference, where the path differences from different slits lead to constructive or destructive interference.

Interference Condition

The interference condition determines the angles at which constructive interference (maxima) occurs. This is typically given by the grating equation m? = d sin?, where m is an integer (the order), ? is the wavelength, d is the spacing between slits, and ? is the angle relative to the normal. The allowed orders are restricted by the fact that |sin?| must be less than or equal to one.

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