How Is the Thickness of an Oil Film Calculated in a Plano-Convex Lens Setup?

[beethoven'smahomeboy]

A plano-convex glass lens of radius of curvature 1.8 m rests on an optically flat glass plate. Before the lens is placed on the plate a film of oil of refractive index 1.78 is deposited on the plate. The arrangement is illuminated from above with monochromatic light of 480-nm wavelength. The indexes of refraction of the lens and plate are 1.5. The radius r of a fringe is related to the thickness t of the film and the radius of curvature R of the lens through r = (2tR)^1/2. What are the radii of the first and second fringes?

How do you determine t?

 

[member 553083]

The thickness of the film of oil can be determined by measuring the gap between the lens and the plate. This can be done with a caliper or other precision measuring device. Once the thickness is known, the radii of the first and second fringes can be calculated using the equation r = (2tR)^1/2, where R is the radius of curvature of the lens (1.8 m in this case). For the first fringe, r = (2*t*1.8)^1/2 and for the second fringe, r = (4*t*1.8)^1/2.