hi guys ! formula for thin film interference class 12 physics wave optics
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Answers
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.
Thin-film interference is a common occurrence that happens in our everyday lives. For instance, you must have noticed some rainbow-coloured reflection in a pool of water on the side of the road or in a bubble. This observable effect is known as thin-film interference.
It occurs mostly when light is reflected several times off (interference) the sides of thin transparent material. However, this is a simple explanation. We shall study more in-depth about this concept below.
Table of Content
What is Thin Film Interference?
Conditions for Interference
Phase Difference and Path Difference
Derivation of Path Difference
Thin-film Interference Soap Bubble
Thin-film Interference Problems and Solutions
What is Thin Film Interference?
Thin-film interference is the phenomenon that is a result of lightwave being reflected off two surfaces that are at a distance comparable to its wavelength. When light waves that reflect off the top and bottom surfaces interfere with one another we see different coloured patterns. During this, the light reaches the boundary between two media and part of it gets reflected and some part gets transmitted.
When the second medium is a thin film, there are two reflections occurring close together at the top and bottom boundary surfaces of the thin film. Thus, there are two waves emerging from a thin film – one wave reflected off the top surface of the film and the other reflected off the bottom surface.
Two waves emerging from a thin film
Meanwhile, the type of interference that can take place is dependent upon these factors.
Wavelength and angle of the incident light.
The thickness of the film.
Refractive indices of the material on either side of the film.
Index of the film medium.
Also Read: Wave Optics
Conditions for Interference
An important consideration in determining thin-film interference is also by knowing the source of the light. A source could be a monochromatic or broadband source. Monochromatic source results in interference patterns that appear as light or dark bands. Broadband source causes the interference patterns to appear as colourful bands.
We will look at the major conditions for interference and get a better idea of the concept.
The form of reflection undergo by the light waves at each boundary depends on the refraction indexes of the two mediums.
Soft reflection: Reflects off a medium with a lower refraction index, as a result, no phase shift is observed.
Hard reflection: Reflects off a medium with a higher refraction index, as a result, a phase shift is observed of λ/2.
Reflection of Light
In this case, there is no phase change due to reflection at B and C because in both cases light is travelling from denser to rarer medium. Thus, the effective path difference between transmitted rays is also 2µt cos r.
For constructive interference,
(2n + 1) λ / 2 = 2μt Cos r
2t = mλn
For destructive interference,
nλ = 2μt Cos r
2t = \left (
When light is travelling from denser medium to rarer medium, the phase shift is zero. When light is travelling from rarer medium to denser medium, the phase r air-film interface will keep moving to the sed as
2 \mu t cos r = \left ( 2n-1 \right )\frac{\lambda }{2}2μtcosr=(2n−1)
2
λ
μ = Refractive index of the film relative to the surrounding
t = Thickness of film and
r = Angle of refraction
For normal incidence, r=0
2\mu t = \left ( 2n-1 \right )\frac{\lambda }{2}2μt=(2n−1)
2
λ
, n=0,1,2….
For minimum thickness, n=1
2\mu t_{min} =
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