Question

All questions of this quiz are about the same film with index of refraction 1.3 which is illuminated with colors red of the wavelength 650 nm and blue of 390 nm wavelength. This film is positioned with upper surface contacting the air and lower surface contacting oil with index of refraction 1.22. What is the minimum thickness of this film which will provide strong reflection in magenta color? (magenta color occurs if you are mixing red and blue)

a. 325 nm
b. 98 nm
c. 125 nm
d. 0 250 nm
e. 150 nm
f. there is no such possibility
g. 975 nm
h. 75 nm
i. 750 nm
j. 195 nm
k. 375 nm

Answer 1

j. 195 nm

Step-by-step explanation:

wave length of magenta colour = average of wavelength of red and blue colour.

=
`(650+390)/(2)`

= 520 nm

medium of lower refractive index are lying on either side of film

For constructive interference

2μ t = (2n+1) λ/2

μ is refractive index of the medium

t is required thickness ,

n is order of fringe ,

Putting the values

2 x 1.3 x t = 1 /2x 520 nm , for n = 0

t =
`(520)/( 2 *1.3* 2 )`

= 100 nm

So thickness will be 100 nm or its odd multiple ( if n = 1 ,2 , 3 etc)

100 , 300 , 500 ,700 ,900 nm .

None of the answer is correct.