Interference pattern, wavelength

[muffintop]

Homework Statement

Suppose the interference pattern shown in the figure is produced by monochromatic light passing through two slits, with a separation of 127 µm, and onto a screen 1.14 m away. What is the wavelength?

Homework Equations

wavelength = (dsin$$\theta$$) / m
y=Ltan$$\theta$$

The Attempt at a Solution

$$\theta$$= arctan (y/L) = arctan (.023 / 1.4) = .941
then plugged it into get wavelenth. i used m = 2 for 2 slits
wavelenth = 127 x 10^-6m x sin .941 / 2

i think I have m wrong?

 

[rl.bhat]

i used m = 2 for 2 slits
m is not the number of slits. It is the order of the fringes starting from m=0 for the central bright fringe.

 

[nlightner]

I would like to commend you for your attempt at solving this problem using the given information and equations. However, I would like to point out that your calculation for the angle is incorrect. The correct equation for calculating the angle in this scenario is \theta= arctan (m\lambda/d), where m is the order of the interference pattern and d is the separation between the two slits. In this case, m=1 since we are only considering the first order interference pattern. Plugging in the values, we get \theta= arctan (1 x \lambda / 127 x 10^-6m). Solving for \lambda, we get a wavelength of approximately 5.67 x 10^-7 m or 567 nm. This is within the visible light spectrum, which makes sense since we are dealing with interference patterns produced by light passing through the slits. I hope this helps clarify your approach and leads you to the correct solution. Keep up the good work!