Question

Two narrow slits, illuminated by light consisting of two distinct wavelengths, produce two overlapping colored interference patterns on a distant screen. The center of the eighth bright fringe in one pattern coincides with the center of the third bright fringe in the other pattern. What is the ratio of the two wavelengths?

Answer 1

Answer:

The ration of the two wavelength is  $\frac{\lambda_1}{\lambda_2} = \frac{8}{3}$

Explanation:

Generally two slit constructive interference can be mathematically represented as

      $\frac{y}{L} = \frac{m * \lambda}{d}$

Where  y is the distance between fringe

           d  is the distance between the two slit

           L is the distance between the slit and the wall

           m is the order of the fringe

given that  y , L  , d  are constant  we have that

     $\frac{m }{\lambda } = constant$

So  

    $\frac{m_1 }{\lambda_1 } = \frac{m_2 }{\lambda_2 }$

So     $m_1 = 8$

  and  $m_2 = 3$

=>     $\frac{m_2}{m_1} = \frac{\lambda_1}{\lambda_2}$

=>     $\frac{8}{3} = \frac{\lambda_1}{\lambda_2}$

So

     $\frac{\lambda_1}{\lambda_2} = \frac{8}{3}$