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Angular Width of a Principal Maximum. Consider N evenly
Chapter 36, Problem 59P(choose chapter or problem)
Problem 59P
Angular Width of a Principal Maximum. Consider N evenly spaced, narrow slits. Use the small-angle approximation sin θ = θ (for θ in radians) to prove the following: For an intensity maximum that occurs at an angle θ, the intensity minima immediately adjacent to this maximum are at angles θ + λ/Nd and θ – λ/Nd, so that the angular width of the principal maximum is 2λ/Nd. This is proportional to 1/N, us we concluded in Section 36.4 on the basis of energy conservation.
Questions & Answers
QUESTION:
Problem 59P
Angular Width of a Principal Maximum. Consider N evenly spaced, narrow slits. Use the small-angle approximation sin θ = θ (for θ in radians) to prove the following: For an intensity maximum that occurs at an angle θ, the intensity minima immediately adjacent to this maximum are at angles θ + λ/Nd and θ – λ/Nd, so that the angular width of the principal maximum is 2λ/Nd. This is proportional to 1/N, us we concluded in Section 36.4 on the basis of energy conservation.
ANSWER:
Solution 59P
The condition for th-order maximum when the phase difference is
for adjacent slits is
. The first minima on either side of the maxima occur when
and
, here
is the number of slits.