Question

A soap film of thickness $0.0011\text{mm}$ appears dark when seen by the reflected light of wavelength $580\text{nm}$. What is the index of refraction of the soap solution, if it is known to be between $1.2$ and $1.5?$

• A. $1.32$
• B. $1.46$
• C. $1.38$
• D. $1.22$

Answer 1

The correct option is A $1.32$

Given :

Thickness of the film, $t=0.0011\text{mm}=0.0011\times {10}^{-3}\text{m}=11\times {10}^{-7}\text{m}$

Wavelength of light, $\lambda =580\text{nm}=580\times {10}^{-9}\text{m}$

For destructive interference,

$2\mu t=n\lambda$

$\Rightarrow \mu =\frac{n\lambda }{2t}=\frac{2n\lambda }{4t}=\frac{2n\times 580\times {10}^{-9}}{4\times 11\times {10}^{-7}}=0.132\left(2n\right)$

Given that index of refraction $\left(\mu \right)$ has a value in between $1.2$ and $1.5$, also $n$ should be an integer.

So, when $n=5$,

$\mu =0.132\times (2\times 5)=1.32$

Hence, option $\left(A\right)$ is the correct answer.