Question

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

• A. 1.32
• B. 1.35
• C. 1.43
• D. 1.48

Answer 1

The correct option is A 1.32

Given $t=0.0011\times {10}^{-3}m$
For minimum reflection of light, $2\mu t=n\lambda$
$\Rightarrow \mu =\frac{n\lambda }{2t}=\frac{2n\lambda }{4t}=\frac{580\times {10}^{-9}\times 2n}{4\times 11\times {10}^{-7}}=0.132\left(2n\right)$
Given that, $\mu$ has value in between 1.2 and 1.5
$\Rightarrow$ When, $n=5,\mu =0.132\times 10=1.32$