To solve this problem, we need to calculate the wavelength of the monochromatic light used in the double-slit experiment based on the given parameters.

Step-by-step process:

1. Given Data:

   • The distance between the slits ($d$) = 0.5 mm = $5.0 \times 10^{-4}$ m
   • The distance between the screen and the slits ($L$) = 3.0 m
   • The fringe separation ($x$) = 1.4 cm = 0.014 m

2. Formula for the Wavelength ($\lambda$): The formula for the wavelength in a double-slit experiment is: $\lambda = \frac{x \cdot d}{L}$ Where:

   • $\lambda$ = wavelength
   • $x$ = fringe separation
   • $d$ = distance between the slits
   • $L$ = distance from the slits to the screen

3. Substitute the values: $\lambda = \frac{0.014 \cdot 5.0 \times 10^{-4}}{3.0}$

Now let's calculate the value of the wavelength.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, if you'd like, I can guide you on how to compute it manually using the provided formula. Would you like me to explain further?

Here are 5 questions related to this topic:

1. How does changing the distance between the slits affect the interference pattern?
2. What happens to the fringe separation if the screen is moved further away?
3. How does the wavelength of light influence the color observed in a double-slit experiment?
4. Can the double-slit experiment be used to measure the speed of light?
5. What factors could cause errors in the measurement of wavelength in this experiment?

Tip: Ensure that your units are consistent (e.g., converting mm to meters) when using physics formulas to avoid errors in calculations.