Approximate Wavelength Formula, λ = ax/D

Approximate Formula for Wavelength (λ = ax/D) from Interference Pattern:

• Where, λ = wavelength

                   a = distance between the 2 coherent wave sources
             
                   x = distance between 2 adjacent antinodal lines
                         (radiating ripples or interference fringes or points of loudness)

                   D = perpendicular distance between the parallel lines
                          where a and x are  measured

• Empirical evidence from experiment shows:

• that x is directly proportional to λ

• that x is inversely proportional to a

• therefore, mathematically, x = kλ/a, where k is found to be = D

• Thus, x = Dλ/a

• And, changing the subject of formula, we have: λ = ax/D

• Application 1: The "Approximate Wavelength Formula, λ = ax/D" can be used to find the wavelength of waves from their interference patterns as a, x and D can be determined from the interference pattern. 

• Application 2: From the same formula λ = ax/D or x = Dλ/a (same formula with different subjects)
• The interference pattern of red, green or blue light can all be explained by the "Approximate Wavelength Formula, x = Dλ/a" 

                        x _red > x_blue

                     

• The distance between adjacent fringes x of red light is bigger than that of green or blue light because the wavelength of red light (λ _red) is longer as compared to that of green light (λ_green) or blue light.

• Since  λ _red > λ_green > λ_blue, from  x = Dλ/a, therefore, x _red > x_green > x_blue.

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