Answer:
The wavelength is [tex]\lambda = 612nm[/tex] and the color is Orange
Explanation:
from the question we are told that
The thickness is [tex]D = 115 nm = 115 *10^{-9} \ m[/tex]
The refractive index of water is [tex]n_w = 1.33[/tex]
Generally the condition for constrictive interference is
[tex]2 * D = \frac{\lambda _n}{2}[/tex]
Where [tex]\lambda _n[/tex] is the wavelength of light in a particular medium
Now considering the medium of water(soap bubble )
The wavelength of light in this medium is mathematically represented as
[tex]\lambda = \frac{\lambda }{n }[/tex]
So
[tex]2 * D = \frac{\frac{\lambda }{n} }{2}[/tex]
[tex]2 * D = \frac{\lambda }{2 * n }[/tex]
=> [tex]\lambda = 4 *n * D[/tex]
substituting values
[tex]\lambda = 4 *1.33 * 115*10^{-9}[/tex]
[tex]\lambda = 6.118 *10^{-7} \ m[/tex]
[tex]\lambda = 612nm[/tex]
The color is orange because the wavelength range of yellow is
590–625 nm
