In
a Newton’s ring experiment the radius of curvature R of the
lens is 5.0 m and its
diameter is 20 mm. (a) We
have to find the number of rings that are produced;
(b) and estimate the number of rings that
would be seen if the arrangement were immersed in water
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Solution: Click For PDF Version (a)
In the
Newton’s ring experimental set up, fringes are formed because
of interference of light waves reflected from the top surface of the
glass plate on which the lens is resting and those reflected from
the curved surface of the lens in contact with
the air or other medium filling the gap. The waves that get
reflected from the top of the glass plate undergo an additional
phase change of
It is given that the radius of curvature of the lens R is
and that the radius of the lens r is
Therefore, the maximum gap between the lens and the plate will be
The total
number of Newton’s rings formed can be found from the
condition for constructive interference when the width of the gap is
We calculate
Using
As the first
ring corresponds to
(b)
We note that
the refractive index of water
The total number of Newton’s rings seen when the set up is immersed in water will be 45.
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.
We may assume that the wavelength of the light
used
is 589 nm.
as the refractive index of the incident side is less than that of
the transmitted side. Let the width of the gap between the lens and
the plate be d. The
condition for fringe formation is
.
,
.
.
and the data of the problem, we find
,
and the last ring corresponds to
,
the total number of rings that will be seen in the experimental
arrangement when the gap between the lens and the plate contains air
will be 34.
.
We calculate
.