Question

A thin film with an index of refraction of $1.50$ coats a glass lens. The index of refraction of the glass is $1.60$.
What is the thinnest coating of film that will provide for very strongly reflected $546nm$ light (constructive thin film interference)?

• A. $171nm$
• B. $182nm$
• C. $91nm$
• D. $273nm$
• E. $415nm$

Answer 1

Answer: (B)

$182nm$

Light is entering in a medium of higher refractive index ($n_2=1.60$) from a medium of lower index ($n_1=1.50$), therefore net path difference in the reflected rays from the two interfaces will be equal to $2t$ (where t is thickness of thin film) , because ,

when light goes from air to thin film path shift in reflected ray $={\lambda }^{\prime }/2$,

when light goes from thin film to glass path shift in reflected ray $={\lambda }^{\prime }/2+2t$

for constructive interference,

$2t=m{\lambda }^{\prime }$,

or $2t=m\lambda /n_1$ ,

where ${\lambda }^{\prime }=$ wavelength in thin film ,

$\lambda =546nm\left(given\right)$ wavelength in vacuum ,

for thinnest coating , $m=0\left(minimum\right)$ ,

therefore, $t_{min}=\lambda /2n_1=546/(2\times 1.50)=182nm$