Respuesta :
Answer:
Explanation:
The problem is based on the interference of thin film
Since light is reflected by medium of greater refractive index two times , the condition of destructive interference is given by the following relation .
2 μ t = ( 2n + 1 ) λ / 2
μ is refractive index of film , t is its thickness , λ is wave length of light .
Putting the values in the expression above
2 x 1.3 x t = ( 2n + 1 ) 500 / 2
for second case
2 x 1.3 x t = [ 2(n-1) + 1 ] 700 / 2
( 2n + 1 ) 500 / 2 = [ 2(n-1) + 1 ] 700 / 2
5 ( 2n + 1 ) = 7[ 2(n-1) + 1 ]
10 n + 5 = 14 n -14 + 7
4 n = 12
n = 3
Putting the values of n in the expression
2 x 1.3 x t = ( 2n + 1 ) 500 / 2
2 x 1.3 x t = ( 2x3 + 1 ) 500 / 2
2.6 t = 673 nm .
Answer:
673.08 mm
Explanation:
The condition for destructive interference for the given case is
[tex]L=\left(m+\frac{1}{2}\right) \frac{\lambda}{2 n}[/tex]
Here,
[tex]L[/tex] = Thickness of the film
[tex]\lambda[/tex] = Wavelength.
Now,
For 500 nm wavelength we have
[tex]L=\left(m+\frac{1}{2}\right) \frac{500}{2 \times 1.30}[/tex]
Since there were no destructive interference, therefore, the order of interference was reduced by one when wavelength changes from 500 to [tex]700\ nm[/tex].
Thus, we have
[tex]L=\left(m-1+\frac{1}{2}\right) \frac{700}{2 \times 1.30}[/tex]
Therefore,
[tex]\quad\left(m-\frac{1}{2}\right) \frac{700}{2 \times 1.30}=\left(m+\frac{1}{2}\right) \frac{500}{2 \times 1.30} \\ \Rightarrow 700 m-350=500 m+250 \\ \Rightarrow 200 m=600 \\ \Rightarrow m=3[/tex]
So the thickness is
[tex]L=\left(3+\frac{1}{2}\right) \frac{500}{2 \times 1.30}=673.08\ mm[/tex]
So the thickness of the oil film is [tex]673.08\ mm[/tex]
