Using light of wavelength 600.0nm in a double slit apparatus we find delta x = 1.0cm. If we use the same apparatus for light of wavelength 450.0 nm, what is the new delta x on the screen?
Delta x = L*lambda/d
But L and d are not given, so how do I approach this problem?
To approach this problem, you need to understand the principles behind the double slit apparatus.
The double slit apparatus consists of two narrow slits separated by a distance d. When light passes through these slits, it diffracts and creates an interference pattern on a screen placed some distance L away from the slits. This interference pattern consists of bright and dark regions.
The equation you mentioned, delta x = L * lambda / d, relates the separation between adjacent bright fringes (delta x) on the screen to the wavelength of the light (lambda), the distance between the slits (d), and the distance from the slits to the screen (L).
In this problem, you are given the values of lambda and delta x for one scenario and need to find the new delta x for a different wavelength.
First, let's calculate the value of L * lambda / d for the given scenario using a wavelength of 600.0 nm:
delta x1 = L * lambda1 / d
Next, apply the equation to the other scenario using a wavelength of 450.0 nm:
delta x2 = L * lambda2 / d
We can set up a ratio between delta x1 and delta x2:
delta x2 / delta x1 = (L * lambda2 / d) / (L * lambda1 / d)
The distance L and the separation between the slits d will be the same in both scenarios since we are using the same apparatus. Therefore, in this ratio, they cancel out:
delta x2 / delta x1 = lambda2 / lambda1
Now, you can simply plug in the values:
delta x2 / 1.0 cm = 450.0 nm / 600.0 nm
Simplifying:
delta x2 = 1.0 cm * (450.0 nm / 600.0 nm)
Calculate this expression to find the new delta x for the light of wavelength 450.0 nm in the double slit apparatus.