Concept explainers
(a)
To show: The point where
(a)
Answer to Problem 48AP
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The formula to calculate the intensity of the light is,
Here,
The value of
Substitute
Conclusion
Therefore, the point where
(b)
To draw: Plot
(b)
Answer to Problem 48AP
The graph between
Figure (1)
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The equation of
The solution of both the equation to coincide at a point is ,
So the solution of the transcendental equation is
(c)
To show: The angular full width at half maximum of the central diffraction maximum is
(c)
Answer to Problem 48AP
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The formula to calculate the phase angle is,
Rewrite the above equation for
If the value of
The path covered by the light is symmetric so the phase angle is double the initial value.
Substitute
Conclusion
Therefore, the angular full width at half maximum of the central diffraction maximum is
(d)
The number of steps involved to solve the transcendental equation ϕ = 2 sin ϕ
.
(d)
Answer to Problem 48AP
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The equation of
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The solution of the transcendental equation
Conclusion
Therefore, the number of steps involved to solve the transcendental equation
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