Step 1: Understanding the Concept:
Young's Double Slit Experiment (YDSE) is a famous physics experiment that demonstrates the wave-particle duality of light.
When coherent light from a source passes through two narrow slits, it creates an interference pattern on a screen placed some distance away.
This pattern consists of a series of alternating bright and dark bands, which are known as interference fringes.
The spacing between any two consecutive bright fringes (or two consecutive dark fringes) is called the fringe width, denoted by the symbol \(\beta\).
The fringe width is determined by the physical setup of the experiment: the wavelength of the light, the distance from the slits to the screen, and the distance between the two slits themselves.
If we change any of these parameters, the pattern on the screen will expand or contract accordingly.
Step 2: Key Formula or Approach:
The formula for fringe width (\(\beta\)) in Young's Double Slit Experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
Where:
\(\lambda\) = wavelength of the light used
\(D\) = distance between the slits and the viewing screen
\(d\) = distance between the two slits
Step 3: Detailed Explanation:
From the formula \(\beta = \frac{\lambda D}{d}\), we can see that the fringe width is directly proportional to the wavelength of light.
Mathematically, this is written as:
\[ \beta \propto \lambda \]
This means if we increase the wavelength, the fringes will spread out more on the screen, becoming wider.
In the given problem, it is stated that the wavelength is doubled:
Let the initial wavelength be \(\lambda_{1}\) and the initial fringe width be \(\beta_{1}\).
Let the new wavelength be \(\lambda_{2} = 2 \times \lambda_{1}\).
All other quantities (\(D\) and \(d\)) are kept constant.
Therefore, the new fringe width \(\beta_{2}\) can be calculated as:
\[ \beta_{2} = \frac{\lambda_{2} D}{d} = \frac{(2\lambda_{1}) D}{d} \]
\[ \beta_{2} = 2 \times \left( \frac{\lambda_{1} D}{d} \right) \]
Substituting the value of \(\beta_{1}\):
\[ \beta_{2} = 2 \times \beta_{1} \]
This calculation clearly shows that the fringe width becomes exactly twice its original size.
For example, if you were using blue light (shorter wavelength) and switched to red light (longer wavelength), the pattern on the screen would appear much more spread out.
In our case, doubling the wavelength results in the fringe width becoming "double," which corresponds to option (B).
Step 4: Final Answer:
The fringe width becomes double when the wavelength is doubled.
Therefore, the correct option is (B).