Question

In a two-slit interference pattern, what is the ratio of slit separation to slit width if there are 17 bright fringes within the central diffraction envelope and the diffraction minima coincide with two-slit interference maxima?

Short answer

The ratio of slit separation to slit width is 9.

Step-by-step solution

Identification of given data

The given data can be listed below,

• The number of bright fringe are, $n=17$
• The number of missing fringe is, 2

Concept/Significance of interference

Interference happens when two or more waves that are the same wavelength and frequency combine to generate one wave.

Determination of the ratio of slit separation to slit width

The first one is interference brought on by the two paths' differences, and the second is diffraction in a single slit. For the diffraction patterns initial minima. For m=1 is given by,

$a\sin \theta =\lambda$ …(i)

Here, is the wavelength of the light.

The position of the bright fringes of double slit interference is given by,

$d\sin \theta =m_2\lambda$ …(ii)

Compare equation (i) and (ii) the rat

$m_2=\frac{d}{a}$

Here, d is the slit separation and a is the slit width.

Substitute all the values in the above,

$$\begin{gathered} \frac{\left(19-1\right)}{2}=\frac{d}{a} \\ \frac{d}{a}=9 \end{gathered}$$

Thus, the ratio of slit separation to slit width is 9.