Half-wave loss is the reflection of light from light sparse medium to light dense medium. According to the refractive index given in the title, we can know that the reflection from n 1 to n2 and n2 to n3 has half-wave loss, so this extra phase difference can cancel each other out, and only the phase difference caused by film thickness needs to be considered in the interference.

The phase difference between the two surfaces in the center of the first dark pattern is 180 degrees, corresponding to half a wavelength. The length of this half wavelength in n2 medium is the half wavelength in vacuum (λ/2)/N2 = λ/2n2. Because light is generated back and forth in the thin film, the thickness of the thin film here is half λ/4n2 of the half wavelength in the above medium.

Similarly, the phase difference between the two surfaces in the center of the second dark pattern is 360+ 180 degrees, corresponding to 1 wavelength+half a wavelength, that is, 3λ/2n2, where the film thickness is 3λ/4n2; ;

The phase difference between the two faces in the center of the third dark pattern is 720+ 180 degrees, corresponding to two wavelengths+half a wavelength, that is, 5λ/2n2, where the film thickness is 5λ/4n2; ;

The fourth dark stripe corresponds to 3 wavelengths+half a wavelength, that is, 7λ/2n2, where the film thickness is 7 λ/4n2; The fifth dark stripe corresponds to four wavelengths+half a wavelength, that is, 9λ/2n2, where the film thickness is 9λ/4n2.