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In a double-slit experiment, light from two monochromatic light sources passes through the same double slit. The light from the first light source has a wavelength of 629 nm. Two different interference patterns are observed. If the 7th order bright fringe from the first light source coincides with the 8th order bright fringe from the second light source, what is the wavelength of the light coming from the second monochromatic light source

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We will determine the wavelength through the relationship given by the distance between slits, this relationship is given under the function

[tex]y = \frac{m\lambda}{d}[/tex]

Here,

m = Number of order bright fringe

[tex]\lambda[/tex] = Wavelength

d = Distance between slits

Both distance are the same, then

[tex]y_1 = y_2[/tex]

[tex]\frac{m_1\lambda_1 r}{d} = \frac{m_2\lambda_2 r}{d}[/tex]

[tex]\frac{m_1\lambda_1}{m_2\lambda_2} =1[/tex]

 Rearranging to find the second wavelength

[tex]m_1 \lambda_1 = m_2 \lambda _2[/tex]

[tex]\lambda_2 = \frac{m_1\lambda_1}{m_2}[/tex]

[tex]\lambda_2 = \frac{7(629)}{8}[/tex]

[tex]\lambda_2 = 550.3nm[/tex]

Therefore the wavelength of the light coming from the second monochromatic light source is 550.3nm