Text: Light of wavelength 558 nm passes through two narrow, closely spaced slits. A double slit interference pattern is observed on a screen located 8.4 m away from the slits. The distance between the central bright spot and the first-order bright spot is 1.42 m. What is the spacing d between the two slits?
Workout:
1. Light of wavelength 558 nm passes through two narrow, closely spaced slits.
2. A double slit interference pattern is observed on a screen located 8.4 m away from the slits.
3. The distance between the central bright spot and the first-order bright spot is 1.42 m.
4. What is the spacing d between the two slits?
Solution:
To find the spacing d between the two slits, we can use the formula for the double slit interference pattern:
d * sin(theta) = m * lambda
where:
- d is the spacing between the slits
- theta is the angle between the central bright spot and the first-order bright spot
- m is the order of the bright spot (in this case, m = 1)
- lambda is the wavelength of light (558 nm)
We are given that the distance between the central bright spot and the first-order bright spot is 1.42 m. Let's call this distance D.
Using trigonometry, we can find the value of sin(theta):
sin(theta) = D / distance to screen
= 1.42 m / 8.4 m
= 0.169
Now, we can rearrange the formula to solve for d:
d = (m * lambda) / sin(theta)
= (1 * 558 nm) / 0.169
= 3301.78 nm
Therefore, the spacing d between the two slits is approximately 3301.78 nm.