air wedge

Interference at an

Air-wedge

FrancisLDept of

Physics GFGC

Newtons rings are formed when a plano-convex lens of large radius of curvature is

placed on a plane glass sheet The combination forms a thin circular air film ofvariable thickness in all directions around the point of contact of the lens and the glassplate at OIf monochromatic light is allowed to fall normally (fig3a)on the lens using the 45ordminclined glass plate and the film is viewed in reflected light interference fringes areobserved in the form of a series with concentric rings( fig3b)

when the light is incident on the plano-convex lens part ofthe light incident on the system is reflected from glass-to-airboundary (say at point D)The reminder of the light istransmitted through the air film it is again reflected fromthe air-to-glass boundary (say from point J)The two rays are (1 and 2 ) reflected from the top andbottom of the air film interfere with each other to producedarkness and brightness The condition For destructive interference is the sameobtained from the air wedge experiment2t 1051980 mλ Figure4To determine the wave length of the sodium light we use the following relationr1051980 1051980 mλR(r) is the radius of the fringe(m) is the order of the ring(R) is the radius of curvature of the plano convex lens(λ )is the wave length of the used monochromatic light (sodium) in vacum

PHASE CHANGE of a light wave due to REFLECTION

bull EXTERNAL REFLECTION (ie from outside surface of material) bull n₁ltn₂ bull180deg (ie π) PHASE CHANGE on reflection of e-m wave

bull INTERNAL REFLECTION (ie from inside surface of material) bull n₁gtn₂ bull NO PHASE CHANGE on reflection of e-m wave

AIR WEDGEWEDGE SHAPED THIN FILM

Let an air wedge be formed between two glass plates slightly inclined to each other at an angle Ɵ as shown

Illuminate the wedge by a parallel beam of monochromatic light Interference occurs between the rays reflected from the upper and lower surfaces of the air film

Alternate dark and bright bands of equal width are observed

OA and OB are two plane surfaces inclined at a very small angle Ɵ such that it encloses a wedge shaped air film

The thickness of the air film increases from O to Awhen illuminated with a monochromatic source

A system of equidistant fringes parallel to the line of intersection of the plane surfaces is observed

Let the mth bright fringe occur at Pm where the thickness is Pm Qm

Condition for a bright fringe 2ntcosr = (2m+1)λ2for small angle of incidence cosr = 1 n = 1 for air and t = Pm Qm

2PmQm = (2m+1)λ2 ----------------1

For the next bright fringe (m+1)

2Pm+1Qm+1 = (2m+3)λ2 ---------------2

Subtracting 1 from 2Pm+1Qm+1 - PmQm = λ2

Which means that the next bright fringe will occur at the point where the thickness of the air ndash film increases by λ2

similarly Pm+2Qm+2 - PmQm = 2λ2----in general for the (m+k)th bright fringe at Pm+k

Pm+k Qm+k - PmQm = k λ2

From the geometry of the figure Let the distance bw Qm Qm+k = x

tanƟ =

for small angles of Ɵ tanƟ asymp Ɵ

Ɵ = x= Fringe width β = (xk) =

If the wedge is formed by placing a thin wire or paper of thickness d bw OA and OB then Ɵ = dl where l is the length of the wedge(air-film)

β = or d =

Applications of air wedge1)Determination of thickness (diameter) of thin objectsThe given object is placed between two glass plates to form an air wedge On illumination we can see alternate bright and dark bands with bandwidth β =λ 2Ɵ

From figureƟ = dLβ = λL2d Or d = λL2β2)Testing of optical flatness of surfaces

A surface is said to be optically flat if it is plane upto 110 th of the wavelength of light usedIn order to test the flatness The surface to be tested is placed in contact with an optically flat glass plate and the fringes are viewed IF THE FRINGES OF EQUAL THICKNESS ARE FORMED THEN THE SURFACE IS FLAT Irregular and distorted fringe pattern is obtained if the surface is not flat

Optical FlatsPRECISION OPTICAL FLATS

The amount of curvature that is shown by the interference bands can be used to determine the

flatness of the surface