Concept explainers
(a)
To show: The condition for a constructive bright interference ring, thickness
(a)
Explanation of Solution
Introduction:
The given arrangement of Newton’s ring apparatus which consists of a plano-convex glass lens of radius of curvature R placed on a flat horizontal glass plate (Refer Figure 33-42) is similar to that of thin film arrangement with a difference that here the film is air of variable thickness
Therefore, the phase change takes place at the top of the horizontal glass plate is
Write the expression for the thickness of the thin glass plate in constructive interference.
Here,
Simplify the above expression and rearrange the terms for thickness.
where
Conclusion:
Thus, the condition for a constructive bright interference ring, thickness
(b)
To show: The relation between radius of the fringe
(b)
Explanation of Solution
Introduction:
The given arrangement of Newton’s ring apparatus which consists of a plano-convex glass lens of radius of curvature R placed on a flat horizontal glass plate (Refer Figure 33-42) is similar to that of thin film arrangement with a difference that here the film is air of variable thickness
Therefore, considering the geometry of plano-convex glass lens and the horizontal glass plate on which the lens arrangement is placed.
Write the expression for the radius of curvature.
Here
Simplify and expand the above expression as:
When
Write again the above expression forradius of curvature.
Simplify the above expression forthe radius of fringe.
Conclusion: Thus, for
(c)
The number of bright fringes obtained in the reflected light.
(c)
Explanation of Solution
Given:
The radius of curvature of the plano-convex lensis
The diameter of the lensis
The wavelength of the light used is
Formula used:
Write the expression for the radius of curvature.
Here
Simplify and expand the above expression as:
When
Write again the above expression forradius of curvature.
Simplify the above expression forthe radius of fringe.
Write the expression for the thickness of the thin glass plate in constructive interference.
Here
Simplify the above expression and rearrange the terms for thickness.
where
Substitute
Rearrange the above expression for the number of fringes.
Calculation:
Substitute
Conclusion:
Thus, there are
(d)
The diameter of the sixth bright fringe.
(d)
Explanation of Solution
Given:
The value of
The radius of curvature of the plano-convex lensis
The wavelength of the light used is
Formula used:
Write the expression for the radius of curvature.
Here
Simplify and expand the above expression as:
When
Write again the above expression forradius of curvature.
Simplify the above expression forthe radius of fringe.
Write the expression for the thickness of the thin glass plate in constructive interference.
Here
Simplify the above expression and rearrange the terms for thickness.
where
Write the expression for the diameter
Substitute
Substitute
Calculation:
Substitute
Conclusion:
Thus, the diameter of the sixth bright fringe is
(e)
The qualitative changes occur in the bright fringe pattern when air is replaced by the water between the two glass plates.
(e)
Explanation of Solution
Given:
The wavelength of the light used is
The refractive index of the glass plates,
Formula used:
Write the expression for wavelengthof the light in the film.
Rearrange the above expression for refractive index.
Calculation:
Substitute
Conclusion:
Thus, the number of bright fringe pattern increased by a factor of
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Chapter 33 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
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