Two waves of light in air have the same wavelength and are intially in phase. They then travel through plastic layers with thickness of `L_(1) = 3.5 mm` and `L_(2) = 5.0 mm` and indices of refraction `n_(1) = 1.7` and `n_(2) = 1.25` as shown in figure. The rays later arrive at a common point. The longest wavelength of light for which constructive interference occurs at the point is

Options

A. `0.8 m m`
B. `1.2 m m`
C. `1.7 m m`
D. `2.9 m m`

Answer

b

Explanation

`Delta x = `path difference between two light waves
`= [n_(1) L_(1) + L_(2) - L_(1)] - [n_(2) L_(2)]`
`Delta phi =` phase difference between two waves
For longest wavelengths, `Delta phi` is the smallest.
For constructive interference, `Delta phi = 2 pi`
`I_(max) = n_(1) L_(1) - n_(2) L_(2) + (L_(2) - L_(1))`
`(1.7) (3.5 xx 10^(-6)) - (1.25) (5.0 xx 10^(-6))`
`+ (5.0 - 3.5) xx 10^(-6)`
` = (5.95 - 6.25 + 1.5) xx 10^(-6) = 1.2 5 10^(-6)m`
`= 1.2 mu m`