21) In figure (a) at the right, a glass lens (n> 1) has a flat top surfaceand a spherical bottom surface with radius of curvature R. Thebottom surface of the lens sits on a flat glass plate (n > 1). In airabove the lens, light with wavelength 2 in air is incidentperpendicularly onto the top surface of the lens. Figure (b) at theright shows a photo taken from above, looking down through thelens. In the photo, we can see circular bright and dark rings (calledNewton's rings) caused by interference of the reflected light due tothe varying thickness of the thin film of air between the lens andthe plate.a) (i) Show that radii r of the bright rings (interference maxima)IncidentlightGlassAirGlass(a)are given by the equation r=R²-maR-where4m=1,3,5,..., assuming that r << R. (ii) Show that, becauseRm11<< R, this reduces to r=,2

i) Applying Pythagoras theorem, r2=R2-R-d2 ...(1) For bright fringes, 2μd=mλ2, where m=1, 3,5

Answered: 21) In figure (a) at the right, a glass…

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