Light with a wavelength of 550 nm is incident normally on a thin soap film (refractive index 1.33) in air.
Adjust conditions:
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膜厚を103.4 nmから2倍にすると、反射光の強さは何倍になるか？
白色光でも、膜厚を103.4 nmから2倍にすると反射光はすべて消えるか？
The equations explain the phenomenon
1The speed and wavelength of light in a material are determined.n=cv……
2The optical path difference between the reflected rays is determined from the round-trip distance inside the film.Optical path difference:2 n d……
3The condition for constructive interference includes the reversal of crests and troughs on reflection.2 n d=(m + ½) λ……
4Derive the condition for destructive interference and apply it to a film with twice the thickness.2 n d=m λ……
5White light reveals how the color of the reflected light depends on film thickness.λ=2ndm + ½……
Related phenomena: refraction, rainbows, lenses, diffraction, and polarization
6Expressing the speed of light in terms of refractive index gives the law of refraction.n₁ sinθ₁=n₂ sinθ₂……
7The condition for total internal reflection is determined for light traveling from water toward air.sinθc=1n……
8Raindrops separate colors.Red 42.4°，Violet 40.7°……
9A lens forms an image.1a+1b=1f……
10Light passes through 2 slits.Δx=L λd……
11An array contains many slits.d sinθ=m λ……
12Polarizers are placed in succession.I=I₀ cos²θ……
What this chapter has shown
Light reflected from the front surface of the film interferes with light returning from inside it. The optical path difference 2nd and the phase changes on reflection determine the intensity of the reflected light at each wavelength. Variations in film thickness cause the reflected color to vary across the film.
0.00 times the original intensity550 nm · ratio to the original intensity
At this thickness, the reflected light cancels out at 550 nm. With white light, other colors remain.
In everyday lifeAntireflection coatings on camera lenses also use thin films to make reflected light cancel out.
Detailed summary
When light slows down in a material, its wavelength decreases. In a thin film, light reflected from the front surface overlaps with light returning from the back surface. The optical path difference 2nd, which depends on the film's thickness, determines which colors undergo constructive or destructive interference. This is why a soap bubble, whose thickness varies across its surface, appears colorful. The same slowing of light also gives rise to refraction, total internal reflection, and rainbows, while the superposition of light passing through narrow openings produces bright and dark fringes. Polarization shows that light is a transverse wave.