Question

Coherent light that contains two wavelengths 670 nm (red) and 470 nm (blue) passes through two parallel slits separated by 0.60 mm. The interference pattern is observed on a screen 90.0 cm from the slits. In the resulting interference pattern, find the distance between the 3rd bright fringe above the central bright fringe for red and the 3rd dark fringe below the central bright fringe for blue

Answer 1

Lambda_1 = 670 nm = 670 times 10^- 3 m lambda_2 = 470 nm = 470 times 10^- 3 m d = 0.60 nm = 0.60 times 10^- 3 m L = 90 cm = 90 times 10^- 2 m Now y = K (A L)/d K is order of bright fringe for lambda_1 = 670 times 10^- 9 times 90 times 10^- 2/0.60 times 10^- 3 y_1 = 3.015 times 10^3 m & So, lambda_2 = 470 times 10^- 3 m & K = 3 y_2 = 3 times 470 times 10^- 9 times 90 times 10^- 2/0.60 times 10^- 3 y_2 = 2.115 times 10^- 3 m therefore delta y = y_1 - y_2 delta y = (3.015 - 2.115) times 10^- 3 delta y = (3.015 - 2.115) times 10^- 3 delta y = 0.9 times 10^- 3 m delta y = 0.9 mm