In Young.s double slit experiment the band width is minimum for the colour

Options

A. red
B. yellow
C. green
D. blue

Answer

To solve the question regarding which color has the minimum bandwidth in Young's double slit experiment, we can follow these steps:

### Step 1: Understand the Concept of Bandwidth
In Young's double slit experiment, the bandwidth (β) of the interference pattern is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = bandwidth
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

### Step 2: Analyze the Relationship Between Bandwidth and Wavelength
From the formula, we can see that the bandwidth (β) is directly proportional to the wavelength (λ). This means that as the wavelength increases, the bandwidth also increases.

### Step 3: Identify the Wavelengths of the Given Colors
The colors of visible light have different wavelengths. The order of colors from longest to shortest wavelength is:
- Red (highest wavelength)
- Yellow
- Green
- Blue (lowest wavelength)

### Step 4: Determine Which Color Has the Minimum Wavelength
Since blue has the shortest wavelength among the colors listed, it will have the minimum bandwidth according to the relationship we established in Step 2.

### Step 5: Conclusion
Thus, in Young's double slit experiment, the bandwidth is minimum for the color blue.

### Final Answer
The color for which the bandwidth is minimum in Young's double slit experiment is **blue**.

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