Two glass microscope slides, of length 10 cm, are in contact at one end and separated by a sheet of paper at the other end, which creates a wedge-shaped film of air. The thickness of the paper is t = 59 μm, and the glass has index of refraction n = 1.5.
Light with wavelength 0.692 μm shines vertically down on the slides. In the resulting interference pattern, what is the distance separating successive dark fringes when viewed from above?
To find the distance separating successive dark fringes, we need to calculate the path difference between the two interfering waves.
The path difference is given by the equation:
Δx = (2t * n) / λ
Where:
Δx is the path difference
t is the thickness of the paper
n is the refractive index of the glass
λ is the wavelength of light
Given:
t = 59 μm
n = 1.5
λ = 0.692 μm
Plugging in these values, we can calculate the path difference:
Δx = (2 * 59 μm * 1.5) / 0.692 μm
Simplifying the equation:
Δx = (2 * 88.5 μm) / 0.692 μm
Δx = 255.20 μm
Now, to find the distance between successive dark fringes, we know that the path difference at a dark fringe is λ/2. Therefore, the distance between successive dark fringes is equal to the path difference at a dark fringe.
So, the distance separating successive dark fringes is:
Distance = Δx = 255.20 μm
Therefore, the distance separating successive dark fringes when viewed from above is 255.20 μm.