A parallel beam of monochromatic light of wavelength 6000 is incident normally on a narrow single slit. The resulting diffraction pattern is focused on a screen using a convex lens of focal length 30 cm placed close to the slit. If the linear width of the central maximum on the screen is found to be exactly equal to the width of the slit, the width of the slit is:

Step-by-step solution

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 a . Therefore: a = 2 f a a^2 = 2 f Given = 6000 = 6 10⁻⁷ m and f = 30 cm = 0.3 m , we substitute these values: a^2 = 2 (6 10⁻⁷ m ) 0.3 m a^2 = 3.6 10⁻⁷ m ^2 = 36 10⁻⁸ m ^2 Taking the square root of both sides: a = 6 10⁻⁴ m = 0.6 mm Answer: 0.6 mm