Question

A soap film (n=1.33) is 805 nm thick. White light strikes the film at normal incidence. You may want to review (Pages 991 - 997) .

Part A

What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides?

If there is more than one answer, separate them by a comma.

? =

713.77,535.33,423.2

  nm  

Answer 1

For constructive interference, the formula to apply is

2nt = (m + .5)?

Start with m = 0

(2)(1.33)(805 X 10^-9) = .5(?)

? = 4.282 X 10^-6 m   (not in the spectrum, not a valid answer)

Try m = 1

(2)(1.33)(805 X 10^-9) = 1.5(?)

? = 1.427 X 10^-6 m   (not in the spectrum, not a valid answer)

Try m = 2

(2)(1.33)(805 X 10^-9) = 2.5(?)

? = 8.565 X 10^-7 m   (not in the spectrum, not a valid answer)

Try m = 3

(2)(1.33)(805 X 10^-9) = 3.5(?)

? = 6.118X 10^-7    which is 611.8 nm - valid answer

Try m = 4

(2)(1.33)(805 X 10^-9) = 4.5(?)

? = 4.758 X 10^-7 m   which is 475.8 nm - valid answer

Try m = 5

(2)(1.33)(805 X 10^-9) = 5.5(?)

? = 3.89 X 10^-7    which is 389 nm

not in visible region [390 nm to 750 nm ]

the wavelength is 611.8 nm nm to 475.8 nm .