A Young's double slit experiment is performed with blue (wavelength 460 nm) and green light (wavelength 550 nm) respectively. If y is the distance of 4th maximum from the central fringe then

Options

A. `y_B=y_G`
B. `y_Bgty_G`
C. `y_Ggty_B`
D. `y_B//y_G= 550//460`

Explanation

To solve the problem of finding the distance of the 4th maximum (Y4) from the central fringe in a Young's double slit experiment using blue and green light, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Fringe Position**:
The position of the nth maximum (Yn) in a Young's double slit experiment is given by the formula:
\[ Y_n = \frac{n \lambda D}{d} \]
where:
- \( Y_n \) = distance of the nth maximum from the central fringe,
- \( n \) = order of the maximum (in this case, \( n = 4 \)),
- \( \lambda \) = wavelength of light,
- \( D \) = distance from the slits to the screen,
- \( d \) = distance between the slits.

2. **Calculate Y4 for Blue Light**:
For blue light with a wavelength \( \lambda_{blue} = 460 \, \text{nm} = 460 \times 10^{-9} \, \text{m} \):
\[ Y_4^{blue} = \frac{4 \cdot \lambda_{blue} \cdot D}{d} = \frac{4 \cdot 460 \times 10^{-9} \cdot D}{d} \]

3. **Calculate Y4 for Green Light**:
For green light with a wavelength \( \lambda_{green} = 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m} \):
\[ Y_4^{green} = \frac{4 \cdot \lambda_{green} \cdot D}{d} = \frac{4 \cdot 550 \times 10^{-9} \cdot D}{d} \]

4. **Compare the Distances**:
Since both expressions have the same factors \( \frac{4D}{d} \), we can compare the wavelengths:
- \( Y_4^{blue} \) is proportional to \( 460 \times 10^{-9} \)
- \( Y_4^{green} \) is proportional to \( 550 \times 10^{-9} \)

Since \( 550 \, \text{nm} > 460 \, \text{nm} \), it follows that:
\[ Y_4^{green} > Y_4^{blue} \]

5. **Conclusion**:
Therefore, the distance of the 4th maximum from the central fringe is greater for green light than for blue light.

### Final Answer:
The distance of the 4th maximum from the central fringe is greater for green light (550 nm) than for blue light (460 nm).

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