As shown in Fig. 40-4, two flat glass plates touch along the...

As shown in Fig. $40-4$, two flat glass plates touch along the leftmost edge and are separated at the other end by a spacer. Using vertical viewing and light with $\lambda=589.0 \mathrm{~nm}$, five dark fringes (indicated by a D in the diagram) are obtained from edge to edge. What is the thickness of the spacer?

Key Concepts

Thin Film Interference

Thin film interference is the phenomenon that occurs when light waves reflected from the upper and lower surfaces of a thin film (or gap) overlap and interfere with each other. This interference leads to patterns of bright and dark fringes depending on the film’s thickness, the wavelength of light, and the difference in optical path the waves travel.

Wedge Interferometer

A wedge interferometer is a setup where two surfaces are arranged at a slight angle to each other, creating a wedge-shaped gap whose thickness varies linearly along one dimension. This variation in thickness produces interference fringes, since different locations along the wedge fulfill the condition for constructive or destructive interference at different orders.

Optical Path Difference

Optical path difference refers to the difference in distance (accounting for the refractive index of the medium) that light travels in two different paths. In thin film and wedge interference, the effective path difference between the beams reflected from the top and bottom surfaces determines whether the light waves interfere constructively or destructively.

Phase Change Upon Reflection

When light reflects from a medium with a higher refractive index, it undergoes a half-wavelength phase shift (180° shift). This additional phase change is crucial when calculating the conditions for interference, as it alters the effective phase difference between the interfering waves and thereby influences the locations of dark and bright fringes.

Fringe Order in Interference Patterns

Fringe order describes the sequence number of an interference fringe (usually labeled by an integer m) that corresponds to a specific condition for constructive or destructive interference. In a wedge interferometer, counting the number of dark or bright fringes across a known distance can be used to determine parameters such as the change in thickness, based on the known wavelength of light.

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