Respuesta :
Answer:
75.19 nm
Explanation:
Condition of constructive interference of the light reflecting from the top of the thin film.
[tex]2ndcos\theta=(m-\frac{1}{2} )\lambda[/tex]
m=1,2,3...
d= thickness of the film
n= refractive index of film
λ= wavelength of the light incident on the film.
for the longest central maximum interference, m=1
⇒[tex]2ndcos\theta=(\frac{\lambda}{2} )[/tex]
⇒[tex]d=\frac{\lambda}{4n} =\frac{700}{4\times1.33}= 131.6\text{_nm}[/tex] nm
similarly, for the same order of reflection the thickness of the film=d'
and wavelength of constructive interference= λ'=400 nm
n=1.33
[tex]2nd'cos\theta=(m-\frac{1}{2} )\lambda'[/tex]
⇒[tex]d'=\frac{\lambda'}{4n}= \frac{400}{4\times1.33}[/tex]= 75.19 nm
Answer:
The difference in thickness is 56.32 nm.
Explanation:
Given that,
Wavelength = 700 nm
Refractive index = 1.33
The constructive interference of light reflecting from the top of thin film
Using formula for constructive interference
[tex]2nd\cos\theta=(m-\dfrac{1}{2})\lambda[/tex]
Where, d = thickness of film
n = refractive index of film
[tex]\lambda[/tex]= wave length of incident light
Here, m= 1,2,3....
For the longest interference, m = 1
[tex]d=\dfrac{\lambda}{4n}[/tex]
We need to calculate the distance
Put the value into the formula of distance
[tex]d= \dfrac{700}{4\times1.33}[/tex]
[tex]d=131.5\ nm[/tex]
(b). Now, wavelength = 400 nm
We need to calculate the distance for same order
Again put the value into the formula of distance
[tex]d'=\dfrac{400}{4\times1.33}[/tex]
[tex]d'=75.18\ nm[/tex]
We need to calculate the difference in thickness
Using formula of thickness
[tex]d''=d-d'[/tex]
[tex]d''=131.5-75.18[/tex]
[tex]d''=56.32\ nm[/tex]
Hence, The difference in thickness is 56.32 nm.
