A parallel beam of white light is incident normally on a water film of thickness 1.0 10⁻⁴ cm . Determine the wavelengths in the visible range ( 400 nm – 700 nm ) that are strongly transmitted by the film. The refractive index of water is 1.33 .

Step-by-step solution

For a thin film of thickness t and refractive index , the condition for constructive interference in the transmitted light (strong transmission) is given by: x = 2 t = n where n = 1, 2, 3, Given: = 1.33 t = 1.0 10⁻⁴ cm = 1000 nm The optical path difference is: 2 t = 2 1.33 1000 = 2660 nm Therefore, the wavelengths that are strongly transmitted are: = 2660 n nm We need in the visible range ( 400 nm to 700 nm ). For n = 4 : = 2660 4 = 665 nm 666 nm For n = 5 : = 2660 5 = 532 nm For n = 6 : = 2660 6 = 443.3 nm 443 nm