Question

You perform a double‑slit experiment in order to measure the wavelength of the new laser that you received for your birthday. You set your slit spacing at 1.05 mm and place your screen 8.91 m from the slits. Then, you illuminate the slits with your new toy and find on the screen that the tenth bright fringe is 4.97 cm away from the central bright fringe (counted as the zeroth bright fringe). What is your laser's wavelength ???? expressed in nanometers?

Answer 1

Answer:

The wavelength is $\lambda = 586nm$

Explanation:

From the question we are told

       The slit spacing is $d =1.05mm = \frac{1.05}{1000} = 1.05*10^{-3}m$

       The distance from the screen $L = 8.91m$

       The distance from central bright fringe $y_n = 4.97cm = \frac{4.97}{100} = 0.0497m$

       The order of the bright fringe $n = 10$

Generally the position of a bright  fringe is mathematically represented as

            $y_n = n\frac{\lambda L }{d}$

            Where  $\lambda$ is the wavelength

             Making $\lambda$ the subject

                        $\lambda = \frac{y_n d}{nL}$

substituting  value

                      $\lambda = \frac{0.0497 * 1.05 *10^{-3}}{10 * 8.91}$

                      $\lambda = 586nm$