Question

In a double slit experiment, if the separation between the two slits is 0.050 mm and the distance from the slits to a screen is 2.5 m, find the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits.(A) 9.0 cm(B) 6.0 cm(C) 1.5 cm(D) 4.5 cm(E) 3.0 cm

Answer 1

Answer:

x = 3 cm

Explanation:

Given that,

The separation between the slits, $d=0.05\ mm=5\times 10^{-5}\ m$

The distance from the slits to a screen, D = 2.5 m

Let x is the spacing between the first-order and second-order bright fringes when coherent light of wavelength 600 nm illuminates the slits, $\lambda=600\ nm=6\times 10^{-7}\ m$

We know that the bright fringe is given by :

$y=\dfrac{n\lambda D}{d}$

So, the spacing between the first-order and second-order bright fringes is :

$x=\dfrac{2\lambda D}{d}-\dfrac{\lambda D}{d}$

$x=\dfrac{\lambda D}{d}$

$x=\dfrac{6\times 10^{-7}\times 2.5}{5\times 10^{-5}}$

x = 0.03 m

or

x = 3 cm

So, the spacing between the first-order and second-order bright fringes is 3 cm. Hence, this is the required solution.