Q. A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm. [Assume that the light is incident nearly perpendicular to the glass surface.]
A) 137.5 nm
B) 275 nm
C) 94.8 nm
D) 68.7 nm
Explanation
[Solution by Dr. Abubacker] Only the air–film reflection suffers a phase change of $\pi$ (the film–glass reflection does not, since $2.0>1.45$). For the two reflected rays, destructive interference (minimum reflection, hence maximum transmission) needs path difference $2nt=m\lambda$; the minimum non-zero thickness is $m=1$: $t=\frac{\lambda}{2n}=\frac{550}{4}=137.5$ nm. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.