Single-Slit Diffraction

Identify slit width a, wavelength lambda and screen distance D, convert to metre, use a sin theta = n lambda for angular minima or y_n = n lambda D/a for screen position, then use twice the first-minimum distance for central maximum width.

Draw a single slit of width a, central axis, screen at distance D, central maximum, first minima on both sides and secondary maxima. Mark angular positions theta and linear distance y from the centre.

A common wrong answer says diffraction disappears when slit width is reduced. Actually, reducing slit width increases spreading, provided light can still pass through the slit.

Single-slit diffraction is the spreading of light after it passes through a narrow slit, producing a broad central maximum and weaker secondary maxima. Minima occur at a sin theta = n lambda for n = 1, 2, 3, ...

Single-slit diffraction is the spreading of light after it passes through a narrow slit, producing a broad central maximum and weaker secondary maxima. Minima occur at a sin theta = n lambda for n = 1, 2, 3, ... Minima: a sin theta = n lambda, where a is slit width in metre, theta is angular position, lambda is wavelength in metre and n = 1, 2, 3, .... For small angles, y_n = n lambda D/a. Central maximum width on screen = 2 lambda D/a. Use these for Fraunhofer diffraction with a narrow single slit and distant screen or lens arrangement. A narrow beam passing through a very thin slit forms a central bright band with faint bands on both sides instead of only a sharp geometrical shadow.

When the slit width is comparable to the wavelength of light, different parts of the same wavefront act as secondary sources and interfere at the screen. The central maximum is brightest and widest because contributions around the straight-through direction mostly reinforce. On either side, minima occur where light from different parts of the slit cancels in pairs. Minima: a sin theta = n lambda, where a is slit width in metre, theta is angular position, lambda is wavelength in metre and n = 1, 2, 3, .... For small angles, y_n = n lambda D/a. Central maximum width on screen = 2 lambda D/a. Use these for Fraunhofer diffraction with a narrow single slit and distant screen or lens arrangement. A slit of width a = 0.20 mm is illuminated by light of wavelength 500 nm. The screen is D = 2.0 m away. Central maximum width = 2 lambda D/a = 2 x 5.0 x 10^-7 x 2.0 / 2.0 x 10^-4 = 1.0 x 10^-2 m = 1.0 cm. The central bright band is about 1.0 cm wide. Questions usually ask for the condition of minima, width of central maximum, effect of changing slit width or wavelength, and comparison with YDSE fringes. A common wrong answer says diffraction disappears when slit width is reduced. Actually, reducing slit width increases spreading, provided light can still pass through the slit.