Question

What is the minimum thickness of a soap bubble needed for constructive interference of reflected light if the light incident on the film is of wavelength $900\text{nm}$ and refractive index of the film is $\mathrm{1.5.}$

• A. $100\text{nm}$
• B. $150\text{nm}$
• C. $200\text{nm}$
• D. $250\text{nm}$

Answer 1

The correct option is B $150\text{nm}$

Given, $\lambda =900\text{nm};\mu =1.5$

For a reflected light, the condition for the constructive interference is,

$2\mu t\cos r=(2n-1)\frac{\lambda }{2}$

$t=\frac{\lambda }{4\mu }(2n-1)\left[\text{For normal incidence i=r=}{0}^{\circ }\right]$

For minimum value of $t,n=1$
$t=\frac{900}{4\times 1.5\times 1}$

$t=150\text{nm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.