When light passes through sequential interfaces, there may be a change of phase upon reflection at each interface. Additionally the wavelength changes with each change of the index of refraction. If the thickness of a thin layer is chosen correctly, then it will serve as an anti-reflective coating bringing about maximally destructive interference between the first and second reflected waves. For convenience, the index of refraction for a variety of materials is provided below. Materials at 20°C for light with a vacuum wavelength of 589 nm. Material n Material n Material n benzene 1.501 diamond 2.419 plexiglas 1.51 carbon disulfide 1.628 fluorite (CaF2) 1.434 quartz (crystalline) 1.544 carbon tetrachloride 1.461 glass (crown) 1.52 quartz (fused) 1.458 ethanol 1.361 glass (flint) 1.66 sodium chloride 1.544 glycerine 1.473 ice (0°C) 1.309 zircon 1.923 water (fresh) 1.333 polystyrene 1.49 air Given that the thin layer of diamond has thickness dd, let mm be an integer. What is the proper condition for the the layer to be an anti-reflective layer? d=mλnwaterd=mλnwater/ndiamondndiamond 2d=mλ2d=mλ/nwaternwater d=(m+12)λnwaterd=(m+12)λnwater/ndiamondndiamond 2d=(m+12)λnwater2d=(m+12)λnwater/ndiamondndiamond d=(m+12)λd=(m+12)λ 2d=(m+12)λ2d=(m+12)λ/nwaternwater 2d=(m+12)λ2d=(m+12)λ/ndiamondndiamond d=mλd=mλ 2d=mλnwater2d=mλnwater/ndiamondndiamond 2d=mλ2d=mλ/ndiamondndiamond

Related questions

Question

When light passes through sequential interfaces, there may be a change of phase upon reflection at each interface. Additionally the wavelength changes with each change of the index of refraction. If the thickness of a thin layer is chosen correctly, then it will serve as an anti-reflective coating bringing about maximally destructive interference between the first and second reflected waves.
For convenience, the index of refraction for a variety of materials is provided below.

Materials at 20°C for light with a vacuum wavelength of 589 nm.

Material	n	Material	n	Material	n
benzene	1.501	diamond	2.419	plexiglas	1.51
carbon disulfide	1.628	fluorite (CaF₂)	1.434	quartz (crystalline)	1.544
carbon tetrachloride	1.461	glass (crown)	1.52	quartz (fused)	1.458
ethanol	1.361	glass (flint)	1.66	sodium chloride	1.544
glycerine	1.473	ice (0°C)	1.309	zircon	1.923
water (fresh)	1.333	polystyrene	1.49	air

Given that the thin layer of diamond has thickness dd, let mm be an integer. What is the proper condition for the the layer to be an anti-reflective layer?

d=mλnwaterd=mλnwater/ndiamondndiamond

2d=mλ2d=mλ/nwaternwater

d=(m+12)λnwaterd=(m+12)λnwater/ndiamondndiamond

2d=(m+12)λnwater2d=(m+12)λnwater/ndiamondndiamond

d=(m+12)λd=(m+12)λ

2d=(m+12)λ2d=(m+12)λ/nwaternwater

2d=(m+12)λ2d=(m+12)λ/ndiamondndiamond

d=mλd=mλ

2d=mλnwater2d=mλnwater/ndiamondndiamond

2d=mλ2d=mλ/ndiamondndiamond

Expert Solution