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Fringes from two slits are observed, using light of wavelengths =370nm and =740nm. At what values...

Fringes from two slits are observed, using light of wavelengths \lambda _{_{1}} =370nm and \lambda _{_{2}} =740nm. At what values for the orders of m, if any, of the two wavelengths do the bright bands (fringes) of the two colors coincide?

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Answer #1

Position of mth order bright fringe is given by

\small y_m = \frac{mL\lambda }{d}

L = distance of screen from slit

d = distance between 2 slits

\small \lambda = Wavelength of light wave used

Let us assume that m1 order bright fringe of \small \lambda_1  coincide with m2 order bright fringe of \small \lambda_2

this implies

\small y_{m_1} = y_{m_2}

\small \frac{m_1L\lambda_1 }{d}= \frac{m_2L\lambda_2 }{d}

\small \frac{m_1L*370 }{d}= \frac{m_2L*740}{d}

\small m_1*370 = m_2*740

\small \frac{ m_1}{ m_2}=\frac{740}{370 }

\small \frac{ m_1}{ m_2}=\frac{2}{1}

Above equation implies that all the orders of  \small \lambda_1 and \small \lambda_2 which are in ratio of 2:1 respectively coincide . For example 2nd order of \small \lambda_1 coincides with 1st order of \small \lambda_2 similarly 4th order of \small \lambda_1 coincides with 2nd order of \small \lambda_2 and so on.

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