Determine the width of the slit in the following case:A narrow single slit is illuminated by infrared light from a helium-neon laser of wavelength 1.15 x 10^-7 m. The centre of the eight dark bands...

Determine the width of the slit in the following case:

A narrow single slit is illuminated by infrared light from a helium-neon laser of wavelength 1.15 x 10^-7 m. The centre of the eight dark bands lies at an angle of 8.4 degrees off the central axis. 

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justaguide | College Teacher | (Level 2) Distinguished Educator

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When monochromatic, coherent light passes through a single slit a series of bright and dark fringes are created on a screen on the other side.

A narrow slit of width a is illuminated by a helium neon laser that has a wavelength 1.15*10^-7 m. The centre of the eight dark band lies at an angle 8.4 degrees off the central axis.

The slit width a, wavelength of light `lambda` , and the angle that a line drawn from the slit to the center of the mth minima makes with the central axis `theta_m` is related by `m*lambda = a sin theta_m` .

Here, `lambda = 1.15*10^-7 m` , `m = 8` , `theta_m = 8.4` degrees. Substituting these values in the formula given earlier.

`8*1.15*10^-7 = a*sin 8.4`

=> a = `6.29*10^-6`

The width of the slit is `6.29*10^-6` m

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