by Bhaskar Department of Physics K L University

Lecture 07 (25 Aug) Interference in Thin Films

Another method for viewing interference is to place a planoconvex lens (L) on top of a flat glass (G) surface. The air film between the glass surfaces varies in thickness from zero at the point of contact to some thickness “d”. A pattern of light and dark rings is observed. These rings are called Newton’s Rings. Newton’s Rings can be used to test optical lenses. Newton Rings

Newton Rings…..

Newton Rings… Ray 1 undergoes a phase change of 180  on reflection, whereas Ray 2 undergoes no phase change R= radius of curvature of lens r=radius of Newton’s ring

Newton Rings… How are these rings are formed? Let us consider a particular point which is at a distance of r from the point of contact of the lens with the glass plate. All points having the same thickness – Destructive Interference. Why are they circular? The locus of all the points from a circular dark ring with ‘r’ as radius. Centre is dark because of phase change during reflection at glass plate.

 For destructive interference  For constructive interference Newton Rings…

Newton Rings….. Conclusion: Fringe width decreases with the order of the fringe and fringes get closer with increases in their order. D 16 -D 9 =2√Rλ >7 Fringes D 9 -D 4 = 2√Rλ >5 fringes D 4 -D 1 = 2√Rλ >3 Fringes

Newton Rings….. Out Comes:  Determination of wavelength of monochromatic source.  Determination of refractive index of liquid.

Determination of wavelength of monochromatic source: Measure the radii or diameter of rings formed Measure the radius of curvature of the lens (R). D n, D m are the diameters of the m th and n th dark rings m D2D2 D 2 vs m R = l²/6h+h/2 Where l is the distance between two legs of spherometer. h is height of convex lens.

Spherometer

Newton Rings… Determination of refractive index of liquid: Liquid

Determination of refractive index ( µ ) of liquid liquid glass plate lens air glass plate lens

Newton Rings… For a air film between the plane convex lens and a flat glass For a liquid medium (whose refractive index is to be measured) between the plane convex lens and a flat glass Resultantly the RI of liquid medium can be written as

1) Optical Testing : Surface Quality a) Flat Surfaces b) Spherical Surfaces c) Surface roughness 2) Direct phase measurements a) phase shiftingphase shifting b) phase stepping 3) Aligning very high quality lenses 4) Space applications a) Radio Astronomy b) Measuring light intensity c) used in retrieving images from telescope Primary Application's of Interferometer

Newton Rings… In white light

light :a wave leading to our future The end

1)In Newton’s ring experiment, the diameter of the 10 th dark ring is 0.433cm. Find the wavelength of incident light, if the radius of curvature of the lens is 70cm. 2)In Newton’s ring experiment, the diameter of the 5 th dark ring was 0.3 cm and the diameter of 25 th ring was 0.8 cm. If the radius of curvature of the plano convex lens is 100cm. Find the wavelength of light used. Problems