Question

What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

Answer 1

Answer:

So visible wavelength which is possible here is

416 nm and 693.3 nm

Explanation:

As we know that for normal incidence of light the path difference of the reflected ray is given as

$2\mu t + \frac{\lambda}{2} = \Delta x$

so here we can say that for maximum intensity condition we will have

$\Delta x = N\lambda$

so we have

$2\mu t + \frac{\lambda}{2} = N\lambda$

now for visible wavelength we have

for N = 1

$2\mu t = \frac{\lambda}{2}$

$\lambda = 4\mu t$

$\lambda = 4(\frac{4}{3})(390 nm)$

$\lambda = 2080 nm$

for N = 2

$\lambda = \frac{4\mu t}{3}$

$\lambda = \frac{4(\frac{4}{3})(390 nm)}{3}$

$\lambda = 693.3 nm$

for N = 3

$\lambda = \frac{4\mu t}{5}$

$\lambda = \frac{4(\frac{4}{3})(390 nm)}{5}$

$\lambda = 416 nm$