A diffraction pattern is obtained using a beam of redlight. What happens if the red light is replaced by blue light

Options

A. No change
B. diffraction bands become narrower and crowded together
C. Bands become broader and farther apart
D. Bands disappear

Answer

To solve the problem of what happens to the diffraction pattern when red light is replaced by blue light, we can follow these steps:

### Step 1: Understand the Concept of Fringe Width
Fringe width (β) in a diffraction pattern is the distance between two consecutive bright or dark fringes. It is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of the light used,
- \( D \) = distance from the slit to the screen,
- \( d \) = distance between the slits.

### Step 2: Identify the Wavelengths of Red and Blue Light
In the visible spectrum:
- The wavelength of red light is approximately 620-750 nm.
- The wavelength of blue light is approximately 450-495 nm.

Since the wavelength of red light is greater than that of blue light, we can denote:
\[ \lambda_{\text{red}} > \lambda_{\text{blue}} \]

### Step 3: Analyze the Effect of Changing Wavelength on Fringe Width
From the formula for fringe width:
\[ \beta \propto \lambda \]
This means that fringe width is directly proportional to the wavelength. Therefore, if we decrease the wavelength (from red to blue), the fringe width will also decrease:
\[ \beta_{\text{red}} > \beta_{\text{blue}} \]

### Step 4: Conclusion on the Diffraction Pattern
Since the fringe width for blue light is smaller than that for red light, the distance between the fringes (bands) will be narrower. This means that the bands will become crowded together.

### Final Answer
When red light is replaced by blue light, the diffraction bands become narrower and crowded together.