The image you uploaded is related to the double-slit interference pattern, and the problem discusses light of two different wavelengths (green and another color) passing through the same slits.

The Problem Breakdown:

a) Wavelength comparison:

The problem first asks whether the wavelength of the second color (likely 455 nm, based on the image) is greater or smaller than 505 nm. We are expected to justify the answer by looking at how the interference fringes change.

b) Calculating the wavelength of the second color:

The second part involves calculating the wavelength of the second color based on the interference pattern. The approximation assumes small angles (small θ), where $\sin \theta \approx \tan \theta$.

Solution Outline:

To address these questions, we need to recall the formula for the position of the interference maxima in a double-slit experiment:

$y_m = \frac{m \lambda L}{d}$ Where:

• $y_m$ is the position of the m-th maximum.
• $\lambda$ is the wavelength of light.
• $L$ is the distance from the slits to the screen.
• $d$ is the distance between the slits.
• $m$ is the order of the maximum.

We can use this formula to analyze the fringe patterns for both wavelengths and compare them to deduce the unknown wavelength and to calculate it.

Let me know if you would like to proceed with the detailed calculations, or if you'd prefer to clarify any part!

Here are some related questions that could be helpful:

1. What determines the distance between interference fringes in a double-slit experiment?
2. How does the wavelength of light affect the angular position of interference maxima?
3. How can you relate fringe width to wavelength in a double-slit setup?
4. What happens to the interference pattern when the wavelength is increased?
5. Can the fringe pattern be used to measure the distance between slits?

Tip: Always check the dimensions and the units in your formulas to ensure they match for accurate results!