Question

Green light of wavelengths 100å from a narrow slit is incident on a double slit. If the overall separation of 10 fringes on a screen 200 cm away is 2cm, find the slit separation.

Answer 1

The answer to the question is $\ 10^{-5}\ m$

CALCULATION:

The wavelength of the green light $\lambda=\ 100\ A^{0}$

                                                                      =$100\times 10^-10\ m$

                                                                      =$10^-8\ m$

The distance between screen and slit is given as D = 200 cm.

                                                                                      = 2 m.

The separation between 10 fringes is given as 2 cm.

Hence, the fringe width is calculated as $\beta=\frac{2}{10}\ cm$

                                                                               $=\ 0.2\ cm$

                                                                               $=\ 0.002\ m$

We are asked to calculate the slit width [ d ].

The fringe width is calculated as follows -

                                                    $\beta=\frac{\lambda D}{d}$

                                                   ⇒ $d=\frac{\lambda D}{\beta}$

                                                             $=\ \frac{10^-8\times 2}{0.002}\ m$

                                                             $=\ 10^{-5}\ m$    [ans]

Answer 2

Answer:

The distance between screen and slit is given as D = 200 cm. = 2 m. The separation between 10 fringes is given as 2 cm.