AP EAMCET Engineering 23 Sep 2020 Shift 1 Paper

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.