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Want to cite, share, or modify this book? This book uses the This equation, derived from classical physics and using wave phenomena, infers that as wavelength increases, the intensity of energy provided will decrease with an inverse-squared relationship. This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. The prevailing theory at the time of Max Planck’s discovery was that intensity and frequency were related by the equation I 2 k T 2. Since the arc subtends an angle ϕ ϕ at the center of the circle, To calculate the intensity at an arbitrary point P on the screen, we return to the phasor diagram of Figure 4.7. In solving that problem, you will find that they are less than, but very close to, ϕ = 3 π, 5 π, 7 π, … rad. The exact values of ϕ ϕ for the maxima are investigated in Exercise 4.120. As a result, E 1 E 1 and E 2 E 2 turn out to be slightly larger for arcs that have not quite curled through 3 π 3 π rad and 5 π 5 π rad, respectively. Since the total length of the arc of the phasor diagram is always N Δ E 0, N Δ E 0, the radius of the arc decreases as ϕ ϕ increases. These two maxima actually correspond to values of ϕ ϕ slightly less than 3 π 3 π rad and 5 π 5 π rad. The proof is left as an exercise for the student ( Exercise 4.119). In part (e), the phasors have rotated through ϕ = 5 π ϕ = 5 π rad, corresponding to 2.5 rotations around a circle of diameter E 2 E 2 and arc length N Δ E 0. The amplitude of the phasor for each Huygens wavelet is Δ E 0, Δ E 0, the amplitude of the resultant phasor is E, and the phase difference between the wavelets from the first and the last sources is The phasor diagram for the waves arriving at the point whose angular position is θ θ is shown in Figure 4.7. This distance is equivalent to a phase difference of ( 2 π a / λ N ) sin θ. If we consider that there are N Huygens sources across the slit shown in Figure 4.4, with each source separated by a distance a/N from its adjacent neighbors, the path difference between waves from adjacent sources reaching the arbitrary point P on the screen is ( a / N ) sin θ. To calculate the intensity of the diffraction pattern, we follow the phasor method used for calculations with ac circuits in Alternating-Current Circuits. Calculate the wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 m. Find the wavelength of light that has its third minimum at an angle of 48.6º when it falls on a single slit of width 3.00 m.

Calculate the intensity relative to the central maximum of an arbitrary point on the screen (b) Find the wavelength of light that has its first minimum at 62.0º.

Calculate the intensity relative to the central maximum of the single-slit diffraction peaks.

By the end of this section, you will be able to:

Intensity equation light wavelength