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Question

(C) When a cylindrical slice is placed on a flat glass plate,the air gap between them forms a wedge-shaped film with a constant thickness along lines

Vedclass · Accepted Answer

The fringe spacing increases as we go outwards.

Vedclass · Answer

(C) When a cylindrical slice is placed on a flat glass plate,the air gap between them forms a wedge-shaped film with a constant thickness along lines parallel to the axis of the cylinder.$1$. The fringes are formed due to the interference of light reflected from the bottom surface of the cylindrical slice and the top surface of the flat glass plate.$2$. Since the thickness of the air film is constant along the direction parallel to the axis,the fringes are straight and parallel to the axis of the cylinder.$3$. At the line of contact,the thickness of the air film is $0$. Since there is a phase change of $\pi$ upon reflection from the glass surface,the path difference is $\lambda/2$,resulting in a dark fringe (destructive interference).$4$. The thickness $t$ of the air film at a distance $x$ from the contact line is given by $t \approx x^2 / (2R)$,where $R$ is the radius of the cylinder. The condition for bright fringes is $2\mu t = (n + 1/2)\lambda$. As $x$ increases,$t$ increases,and the fringe spacing $\Delta x$ actually decreases,not increases. Thus,statement $C$ is incorrect.

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