A monochromatic beam passes through a single slit of width 0.15mm and forms a diffraction pattern on a screen 2.50m away. The distance from the central maximum to the first dark band on one side is measured to be 10.7mm. The distance from the central maximum to the second dark band on the same side is 21.5mm. Assume the approximation for small angles is valid.
(a) Using the first–order dark band, determine the wavelength of the light.
(b) Using the second–order dark band, determine the wavelength of the light.
(c) Calculate the average of the two wavelength values obtained in parts (a) and (b). Determine the percent difference between the two individual values and comment on whether averaging improves precision.
(d) The experiment is now repeated with the same geometry, but the entire apparatus is immersed in a transparent liquid whose index of refraction is 1.46. Predict the distance from the central maximum to the first dark band in the liquid.