Question

A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference of the reflected light is observed for wavelengths of 500 and 700 nm and for no wavelengths in between.If the index of refraction of the oil is 1.30 and that of the glass is 1.50, find the thickness of the oil film.

Answer 1

Answer:

673.08 mm

Explanation:

The condition for destructive interference for the given case is

$L=\left(m+\frac{1}{2}\right) \frac{\lambda}{2 n}$

Here,

$L$ = Thickness of the film

$\lambda$ = Wavelength.

Now,

For 500 nm wavelength we have

$L=\left(m+\frac{1}{2}\right) \frac{500}{2 \times 1.30}$

Since there were no destructive interference, therefore, the order of interference was reduced by one when wavelength changes from 500 to $700\ nm$.

Thus, we have

$L=\left(m-1+\frac{1}{2}\right) \frac{700}{2 \times 1.30}$

Therefore,

$\quad\left(m-\frac{1}{2}\right) \frac{700}{2 \times 1.30}=\left(m+\frac{1}{2}\right) \frac{500}{2 \times 1.30} \\ \Rightarrow 700 m-350=500 m+250 \\ \Rightarrow 200 m=600 \\ \Rightarrow m=3$

So the thickness is

$L=\left(3+\frac{1}{2}\right) \frac{500}{2 \times 1.30}=673.08\ mm$

So the thickness of the oil film is $673.08\ mm$

Answer 2

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 .