A parallel beam of monochromatic light of wavelength 500 nm falls normally on a single narrow slit. A convex lens of focal length 40 cm is placed immediately after the slit to focus the diffraction pattern on a screen. If the linear width of the central maximum is observed to be exactly equal to the width of the slit, the width of the slit is:

Step-by-step solution

Let the width of the slit be a . The linear width of the central maximum in a single slit diffraction pattern focused by a lens of focal length f is given by: W = 2 f a According to the given condition, the linear width of the central maximum is equal to the slit width ( W = a ). Therefore: a = 2 f a a^2 = 2 f Given: = 500 nm = 500 10⁻⁹ m f = 40 cm = 0.4 m Substituting the values: a^2 = 2 (500 10⁻⁹) 0.4 a^2 = 400 10⁻⁹ = 4 10⁻⁷ m ^2 Taking the square root: a = 4 10⁻⁷ m = 2 10⁻⁴ m Converting to millimeters: a = 0.2 m