A monochromatic light beam falls normally on a single slit. The angular spread of the central maximum in the resulting diffraction pattern is observed to be exactly 90^ . The ratio of the slit width to the wavelength of the light is:

Step-by-step solution

The angular spread of the central maximum in a single slit diffraction pattern is given by 2 , where is the angular position of the first minimum. Given that the angular spread is 90^ , we have: 2 = 90^ = 45^ The condition for the first diffraction minimum is: a = where a is the slit width and is the wavelength. Substituting = 45^ : a (45^ ) = a ( 1 2 ) = The ratio of the slit width to the wavelength is: a = 2 Answer: 2