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# thin film(destructive干涉)

air (n=1)

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thin film(n=1.3) 厚: t(m)

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glass(n=1.5)

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2n(film)t = (n+1/2)入

2n(film)t = (n+1/2)入

### 2 個解答

• 最愛解答

I suppose you are talking about destructive interference by reflection at the top and bottom of the thin film.

In applying the equation: 2.n.t = (m+1/2)入

the wavelength of light in air 入(air) should be used.

In fact, the above equation comes from the equation,

2t = (m+1/2)入(film)

where 入(film) is the wavelength of light in the material medium of the film

The term on the left hand side, 2t, is the (geometrical) path difference. The wavelength of light at the medium of intereston should be used on the right hand side. In this case, it is the wavelength at the thin film.

Since when light travels in the film, its speed is reduced but keeping the frequency unchanged, hence we have,

v(film) = f.入(film), where v(film) is the speed of light in the film

When light travels in air, we have, v(air) = f.入(air)

Dividing both equations, v(film)/v(air) = 入(film)/入(air)

i.e. 入(film) = 入(air).[v(film)/v(air)] = 入(air)/[v(air)/v(film)] = 入(air)/n

where n = v(air)/v(film), is the refractive index of the film material

Thus, the destructive interference equation becomes,

2t = (m+1/2)[入(air)/n]

i.e. 2nt = (m+1/2)入(air)

[Note: it is assumed that, to a good approximation, the wavelengths of light in air and vacuum are the same].

• 在 air-thin film 和 thin file-glass 介面反射時, 光皆發生了 phase change π, 所以光程差為半數波長時才會產生相消干涉.

兩條反射光的起點相差了 thin film 厚度的一來一回 (即共兩程), 所以光程差為 2 x thin film 厚度 x thin film 折射率.

2010-03-12 09:15:08 補充：

用 thin film 內的波長, 因為兩道反射光線的程差距離就是差了 thin film 的厚度.

資料來源： Myself