Reflection and Transmission by a Slab

We now consider reflection and transmission of a wave Eiexp[iu(N2z/c — 0] normally incident on a plane-parallel slab of arbitrary material embedded in a nonabsorbing medium (Fig. 2.7). The reflected and transmitted waves are 

The field amplitudes are written as scalars because reflection and transmission at normal incidence are independent of polarization. At the first boundary (z = 0), the amplitudes satisfy the usual boundary conditions  

Transmission experiments are usually carried out with the slab in air (n2 — 1) and are feasible only if a measurable amount of light is transmitted. This in turn requires that for all but very thin samples (say, h X) kx must be small compared with unity. With this restriction p is small compared with and the slab transmittance is to good approximation given by 

Interference bands in slab transmission may be observed because of the oscillatory term cos in (2.75). Transmission maxima occur when f = 2irp( pX = 2nxh), where p = 1,2,3,. ... If a maximum occurs at a wavelength X, neighboring maxima occur at X + AX, where 

If SX AX, distinct interference bands in the transmission spectrum will not be observed in this case slab averaged over the wavelength interval SX is 

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