a) A nonreflective coating ( n = 1.48) covers the glass ( n = 1.52) of a camera
ID: 1381801 • Letter: A
Question
a) A nonreflective coating (n = 1.48) covers the glass (n = 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum = 562 nm), determine the minimum nonzero thickness that the coating can have.
b)Orange light (?vacuum = 610 nm) shines on a soap film (n = 1.37) that has air on either side of it. The light strikes the film perpendicularly. What is the minimum thickness of the film for which constructive interference causes it to look bright in reflected light?
Explanation / Answer
b)
When the light hits the top of the soap film some is reflected off and some is transmitted through into the soap film.the transmitted light then travels through the soap film and reflects off the back of the soap film, and back out of the soap film surface.
What we want is for the first reflected light to constructively interfere with the light that reflects off the back of the soap film. Depending on the thickness of the soap film the light will be either in or out of phase as it travels through the film when it comes out.
the amount of shift a wavelength gets through the film is S:
S = 2d - L/2
where L is the wavelength of light in the film and d is the thickness of the film, 2d because it travels through the film twice once in once out when reflected. L/2 is a phase shift of pi(half a wavelength) that happens when light goes from a low refractive index, n1, to a higher one n2 (omit L/2 if n1 is > n2)
For constructive interference the total amount of S should be equal to an integer number, n, of wavelengths.
S = nL where n = 0,1,2,3,4,5 ......
therefore by equating these 2 we get the following
nL = 2d - L/2
d = L/2 * (n + 1/2)
We also should note that L is the wavelength INSIDE the film, not outside! remember light slows down when in a medium. To find the wavelength of light in a medium you divide the wavelength of the light in a vacumn by the refractive index of the medium.
which in your case is L = 611nm / 1.33
thus min thickness=611/(2*1.37)*1/2=111.49*10^-9 m ...............(n=0 for min thickness)
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