Question

What is the wave length if the distance from the central bright region to the sixth dark fringe is 1.9 cm . Answer in units of nm.

Answer 1

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  wavelength is  $\lambda = 622 nm$

Explanation:

  From the question we are told that

    The distance of the slit to the screen is  $D = 5 \ m$

    The order of the fringe is m  =  6

     The distance between the slit is  $d = 0.9 \ mm = 0.9 *10^{-3} \ m$

    The fringe distance is  $Y = 1.9 \ cm = 0.019 \ m$

Generally the for a dark fringe the fringe distance is  mathematically represented as

        $Y = \frac{[2m - 1 ] * \lambda * D }{2d}$

=>     $\lambda = \frac{Y * 2 * d }{[2*m - 1] * D}$

substituting values

=>      $\lambda = \frac{0.019 * 2 * 0.9*10^{-3} }{[2*6 - 1] * 5}$

=>     $\lambda = 6.22 *10^{-7} \ m$

       $\lambda = 622 nm$