A Newton’s rings apparatus is used to determine the radius of curvature of a lens. The radii of the nth and (n+20)th bright rings are measured and found to be 0.162 cm and 0.368 cm, respectively, in light of wavelength 546 nm. We have to calculate the radius of curvature of the lower surface of the lens.
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Solution: Click For PDF Version We assume that fringes are formed by interference of rays reflected from the top and the bottom of the air gap between the lens and the glass plate.
Let the width
of the air gap where the nth and the (n+20)th bright fringes are
formed be
Let the radii
of the nth and (n+20)th bright fringe be
From geometry we note that
Assuming that
R the radius of
curvature of the lower surface of the lens is much bigger than
the
approximate value of
Similarly, we
note that
Using
monochromatic light of wavelength
Using the condition for bright fringe formation, we write the equation
We us the data of the problem
and find that
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and
,respectively.
and
,
respectively.
,
.
.
the condition for the mth bright fringe in the Newton’s rings
experimental set up is
,
,
and
,