Question

In a double slit interference experiment, the separation between the slits is 1⋅0 mm, the wavelength of light used is 5⋅0 × 10⁻⁷ m and the distance of the screen from the slits is 1⋅0 m. (a) Find the distance of the centre of the first minimum from the centre of the central maximum. (b) How many bright fringes are formed in one centimetre width on the screen?

Answer 1

Given:
Separation between the two slits, $d=1\mathrm{mm}={10}^{-3}\mathrm{m}$
Wavelength of the light used, $\lambda =5.0\times {10}^{-7}\mathrm{m}$
Distance between screen and slit, $D=1\mathrm{m}$
(a) The distance of the centre of the first minimum from the centre of the central maximum, x = $\frac{\mathrm{width}\mathrm{of}\mathrm{central}\mathrm{maxima}}{2}$
That is, $x=\frac{\beta }{2}=\frac{\lambda D}{2d}$ ...(i)
$$\begin{gathered} =\frac{5\times {10}^{-7}\times 1}{2\times {10}^{-3}} \\ =2.5\times {10}^{-4}\mathrm{m}=0.25\mathrm{mm} \end{gathered}$$
(b) From equation (i),
fringe width, $\beta =2\times x=0.50\mathrm{mm}$
So, number of bright fringes formed in one centimetre (10 mm) = $\frac{10}{0.50}=20$.