Double slit experiment and wavelengths

[brunettegurl]

Homework Statement

A double-slit experiment is performed with light of wavelength 558.0 nm. The bright interference fringes are spaced 1.84 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 335.0 nm?

Homework Equations

d= $$\frac{\lambda * L}{spacing}$$

The Attempt at a Solution

so our assumption is that everything stays constant while only the wavelength changes and the fringe spacing..right?? i am unable to think ahead of this point ..pls. help

 

[brunettegurl]

nevermind i made a silly error while trying to set up a ration btw the 2 wavelengths and distances

 

[nlightner]

I can provide an explanation for this phenomenon. The double-slit experiment is a classic experiment in physics that demonstrates the wave-like nature of light. In this experiment, a beam of light is passed through two narrow slits, and the resulting interference pattern is observed on a screen behind the slits. This pattern is characterized by bright and dark fringes, which are a result of constructive and destructive interference of the light waves passing through the slits.

In order to understand the relationship between the wavelength and the fringe spacing, we can use the equation given in the homework statement: d= \frac{\lambda * L}{spacing}. This equation tells us that the fringe spacing (d) is directly proportional to the wavelength (\lambda) and the distance between the slits (spacing), while inversely proportional to the distance between the slits and the screen (L).

In the given scenario, the wavelength is changed from 558.0 nm to 335.0 nm while keeping the other variables constant. This means that the fringe spacing will also change accordingly. Using the equation, we can calculate the new fringe spacing as follows:

d' = \frac{\lambda' * L}{spacing} = \frac{335.0 nm * 1.84 mm}{558.0 nm} ≈ 1.10 mm

Therefore, the new fringe spacing will be approximately 1.10 mm when the light is changed to a wavelength of 335.0 nm. This shows that as the wavelength decreases, the fringe spacing also decreases. This is because shorter wavelengths have a higher frequency and therefore, the waves interfere more frequently, resulting in a smaller fringe spacing.

In conclusion, the double-slit experiment and its results provide strong evidence for the wave-like nature of light and help us understand the relationship between wavelength and fringe spacing. This experiment has been instrumental in shaping our understanding of light and its behavior.