When a light wave of wavelength λ falls at an angle of incidence i on a film of refractive index µ and thickness t, then the condition for constructive interference in the reflected system is 2µi‌cos‌r=(2m+1)‌
λ
2
,m=0,1,2,... For normal incidence, i=r=0 ∴‌‌2µt‌cos‌0=(2m+1)‌
λ
2
⇒‌‌2µt=(2m+1)‌
λ
2
⇒‌‌2t=(2m+1)‌
λ
2
‌‌[becauseµ=1 for air] ⇒‌‌λ=‌
4i
2m+1
=‌
4×2.9×10−7
2m+1
m [∵t=2.9×10−4mm=2.9×10−7m] ⇒‌‌λ=‌
11.6×10−7
2m+1
m For m=0,‌‌λ0=11.6×10−7m=1160nm For m=1,‌‌λ1=‌
11.6×10−7
2×1+1
=386.67nm For m=2,‌‌λ2=‌
11.6×10−7
2×2+1
=232nm Hence, wavelength of blue light of 450nm is closest to λ1=386.67nm. Hence, colour of reflected light is blue.