A wedge shaped air film is made between two sheets of glass using a spacer at one end of the glass sheets. If light of wavelength 589 nm is used to illuminate the plates, how thick is the spacer if five dark fringes are observed between the edges of the glass

1178 nm

Explanation:

We are given that

Wavelength of light=

We have to find the thickness of spacer if five dark fringes are observed between the edges of the glass.

Suppose that first dark fringe and fifth dark fringe near spacer, then the path length of light is 4 times the wavelength of light.

The light passes through air film is two times  then the change in air film thickness  from one edge to other is two times the wavelength of light.

Change in air film thickness  from one edge to other edge  is same as the thickness of spacer.

Therefore, thickness of spacer=

Thickness of spacer=m

Thickness of spacer=1178 nm

Hence, the thickness of spacer=1178 nm

where are the vectors ?