Diffraction by N-slits

Optical disturbance due to N slits

Contribution of j th slit

Contribution of N slits

Irradiance due to N-slits I 0 = I rradiance by single slit at  =0

For principal maxima or

For minima Between consecutive principal maxima, there will be N-1 minima

Subsidiary maxima (N-2) subsidiary maxima between consecutive principle maxima

For large N, irradiance of first subsidiary maxima

Diffraction from multiple slits Slit Diffraction Pattern

Normal incidence Transmission grating

Oblique incidence a

For two wavelengths

Dispersive power of grating Width of principal maxima

Barely resolved ItIt  s  w

Chromatic resolving power of a grating

Chromatic resolving power of a prism

Reflection grating

Diffraction grating

The nominal track separation on a CD is 1.6 micrometers, corresponding to about 625 tracks per millimeter. This is in the range of ordinary laboratory diffraction gratings. For red light of wavelength 600 nm, this would give a first order diffraction maximum at about 22°.

15  15  0 nm 450 nm Atomic Force Microscope Image of CD

Bragg’s law X-ray diffraction from crystals: 2d Sin θ = n λ

Phase grating Delta function Bessel function

Problem Consider a opaque screen with 5 equally spaced narrow slits (spacing between them is d) and with monochromatic plane wave (wavelength ) incident normally. Draw a sketch of the transmitted intensity vs. angle to the normal for  = 0 to  = 1/5 radian. Take Sin  =  over this range and assume d/ =10. What is the ratio of least intense to the most intense peak? What is the angular distance of the first intense peak away from  = 0.