You dip a wire loop into soapy water (n = 1.33)and hold it up vertically to look at the soap film in white light.The soap film looks dark at the top because it has sagged,and its thickness there is nearly zero,causing the reflected wavelengths to interfere destructively.Part way down the loop you see the first red band of the reflected white light.What is the thickness of the soap film there? (Take the wavelength of red light to be 680 nm.)
A)130 nm
B)170 nm
C)220 nm
D)250 nm
E)340 nm

Question

Quizplus · Accepted Answer

The thickness of the soap film for the first red band is calculated using the formula for constructive interference in thin films: $2nt = m\lambda$, where $n$ is the refractive index, $t$ is the thickness, $m$ is the order of interference (for the first band, $m = 1$), and $\lambda$ is the wavelength in the medium. Solving for $t$ gives $t = \frac{m\lambda}{2n} = \frac{1 \times 680 \, \text{nm}}{2 \times 1.33} \approx 170 \, \text{nm}$.

You Dip a Wire Loop into Soapy Water (N =