Respuesta :
Answer:
638 nm
Explanation:
n = index of refraction of soap
m = order
[tex]\lambda _{max}[/tex] = wavelength at maximum interference = 684 nm
[tex]\lambda _{min}[/tex] = wavelength at minimum interference = 570 nm
At constructive interference is given as
2nt = m [tex]\lambda _{max}[/tex] eq-1
At destructive interference is given as
2nt = (m + 0.5) [tex]\lambda _{min}[/tex] eq-2
using eq-1 and eq-2
m [tex]\lambda _{max}[/tex] = (m + 0.5) [tex]\lambda _{min}[/tex]
m (684) = (m + 0.5) (570)
m = 2.5
using eq-2
2nt = (m + 0.5) [tex]\lambda _{min}[/tex]
2(1.34) t = (2.5 + 0.5) (570)
t = 638 nm
The expressions for the interference in thin films allow to find the answer for the thickness of the film with two consecutive interferences is:
t = 638 nm
Given parameters
- Refractive index n = 1.34
- Maximum interference λ₀₂ = 684 nm
- Minimum interference λ₀₁ = 570 nm
To find
- The thickness of the soap film.
The phenomenon of interference in thin films should take into account, see attached.
- There is a phase change of the wave when it passes from a medium with a lower refractive index to one with a higher refractive index.
- The wavelength within the film is moduled by the reactivity index.
λₙ = [tex]\frac{\lambda_o}{n}[/tex]
With these facts the expressions for the interference are:
- Destructive 2nt = (m + ½) λ₀₁
- Constructive 2n t = m λ₀₂
where n is the refractive index, t the thickness of the film, lam the wavelengths and m an integer.
Let's solve for the thickness.
[tex]m = \frac{2nt}{\lambda_{o2}} \\m= \frac{2nt}{\lambda_{o1}} - \frac{1}{2} \\\frac{2nt}{\lambda_{o2}} = \frac{2nt }{\lambda_{o1}} - \frac{1}{2}[/tex]
[tex]t \ 2n ( \frac{1}{\lambda_{o1}} - \frac{1}{\lambda_{02}} )= \frac{1}{2}[/tex]
Let's calculate.
[tex]t\ 2 \ 1.34 ( \frac{1}{570} - \frac{1 }{684} ) = \frac{1}{2}[/tex]
t 7.8362 10⁻⁴ = ½
t = [tex]\frac{1}{2 \ 7.8362 \ 10^{-4}}[/tex]
t = 638.1 nm
In conclusion using the expressions for the interference in thin films we can find the answer for the thickness of the film with two consecutive interferences is:
t = 638 nm
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