In the double slit experiment with light, we know that the spacing of the interference fringes (which is what we call the bright spots on the screen) depends on the wavelength of the light. How? Specifically, if you make the wavelength of the light bigger, how does the spacing of the fringes change?

I'm confused please help!

In the double slit experiment with light, the spacing of the interference fringes or bright spots on the screen is determined by the wavelength of the light. To understand this, let's first explain the basic concept behind the double slit experiment.

In this experiment, light from a single source passes through two narrow slits, creating two coherent light sources. When these two sources overlap, they create an interference pattern on a screen placed behind the slits. This interference pattern consists of a series of alternating bright and dark fringes.

The key to understanding how the spacing of the fringes depends on the wavelength of light lies in the concept of interference. Interference occurs when two or more coherent waves combine and either reinforce each other (constructive interference) or cancel each other out (destructive interference).

Now, let's discuss how the wavelength affects the spacing of the fringes. The spacing between adjacent bright fringes, also known as the fringe separation or fringe spacing, can be calculated using the following formula:

d*sin(θ) = m*λ

Where:
- d is the distance between the two slits,
- θ is the angle between the line connecting the slits and the line from the slits to a specific fringe,
- m is the order of the fringe (0, 1, 2, 3, ...),
- λ is the wavelength of light.

From this equation, we can see that the fringe spacing depends directly on the wavelength of light (λ). When the wavelength is larger, the fringe spacing increases.

Intuitively, we can understand this by thinking about the constructive and destructive interference that occurs between the waves from the two slits. If the wavelength is larger, the waves from the two slits will undergo more complete cycles of the wave before they overlap on the screen. As a result, the interference pattern will have wider bright fringes and, accordingly, wider spacing between adjacent fringes.

To summarize, in the double slit experiment with light, the spacing of the interference fringes depends on the wavelength of light. If the wavelength is bigger, the spacing between the fringes increases.