White coherent light ( 400 nm – 700 nm ) is passed through the slits of a Young's double slit experiment. The separation between the slits is 0.5 mm and the screen is situated 50 cm away from the slits. A hole exists in the screen at a location 1.0 mm away (along the width of the fringes) from the central line. Determine which wavelength(s) will have a strong intensity in the light emerging from the hole.

Step-by-step solution

Given parameters are: Slit separation, d = 0.5 mm = 0.5 10⁻³ m Distance to screen, D = 50 cm = 0.5 m Position of the hole, y = 1.0 mm = 1.0 10⁻³ m The path difference x at a distance y from the central maximum is given by: x = y d D Substituting the given values: x = (1.0 10⁻³) (0.5 10⁻³) 0.5 m x = 1.0 10⁻⁶ m = 1000 nm For strong intensity (constructive interference), the path difference must be an integer multiple of the wavelength : x = n where n = 1, 2, 3, Therefore, the possible wavelengths are: = x n = 1000 n