Question

A thin film of liquid polymer, $n=1.25$ coats a slab of Pyrex, $n=1.50$. White light is incident perpendicularly on the film. In the reflection, full destructive interference occurs for $\lambda =600nm$ and full constructive interference occurs for $\lambda =700nm$. What is the thickness of the polymer film?

• A. $120nm$
• B. $280nm$
• C. $460nm$
• D. $840nm$

Answer 1

The correct option is D $840nm$

For case when wave $R_a$ is in phase with wave $R_b$,

Destructive interference occurs when $2t=(m_1+\frac{1}{2})\frac{{\lambda }_1}{n}$

Constructive interference occurs when $2t=\frac{m_2{\lambda }_2}{n}$

Given : ${\lambda }_1=600nm$

${\lambda }_2=700nm$

$n=1.25$

$m_1$ and $m_2$ have to be integer.

Thus, $(m_1+\frac{1}{2})\frac{{\lambda }_1}{n}=\frac{m_2{\lambda }_2}{n}$

Putting the values , gives $m_1=3and{m}_2=3$

Now from equation, $2t=\frac{m_2{\lambda }_2}{n}$

$2t=\frac{3\times 700nm}{1.25}$ gives $t=840nm$