A transparent film of refractive index 1.4 is coated on a glass plate of refractive index 1.5 . White light is incident normally on the film. In the reflected light, two consecutive missing wavelengths (minimum intensity) are found to be 700 nm and 420 nm . The thickness of the transparent film is:

Step-by-step solution

When light reflects from the air-film interface (refractive index 1.0 to 1.4 ), it undergoes a phase change of . When light reflects from the film-glass interface (refractive index 1.4 to 1.5 ), it also reflects from a denser medium, so it undergoes another phase change of . The relative phase shift between the two reflected waves is 0 . The condition for missing wavelengths (destructive interference) in reflected light with zero relative phase shift is: 2 t = (m + 1 2 ) where m = 0, 1, 2, For the two consecutive m