Why Is the Fringe at the Narrow End of a Wedge Always Dark?

[Vixus]

For a solid wedge of material of length L and maximum width D (ie, a triangle) how would one obtain an equation for /\x, the distance between dark fringes?

For wedge fringes, how come the fringe at the narrow end is always dark?

 

[Doc Al]

You need to consider two factors that determine the phase difference--and thus the interference--between the reflections at each boundary:

What is the phase change upon reflection?

What distance does the light travel in passing (twice) through the wedge?​

Read up with these factors in mind.

 

[kyle8921]

To obtain an equation for the distance between dark fringes in a wedge of material, we can use the principles of diffraction and interference. First, we need to consider the geometry of the wedge. The distance between the dark fringes, /\x, can be determined by the angle of the wedge, the wavelength of light, and the refractive index of the material.

Assuming that the wedge is thin and the light is incident normally, we can use the following equation:

/\x = (wavelength * refractive index) / (2 * tan(angle))

This equation takes into account the fact that the light will be diffracted and interfere as it passes through the wedge, resulting in a series of fringes. The angle of the wedge will determine the spacing between these fringes, with a smaller angle resulting in a larger /\x.

As for the fringe at the narrow end always being dark, this is due to the principle of destructive interference. When the light passes through the wedge, it will be diffracted and split into two beams. These two beams will interfere with each other, resulting in constructive and destructive interference. At the narrow end of the wedge, the two beams will be nearly parallel, causing destructive interference and resulting in a dark fringe.

In summary, the equation for /\x in a wedge of material can be obtained by considering the geometry of the wedge and applying the principles of diffraction and interference. The fringe at the narrow end is always dark due to destructive interference between the diffracted beams.