Double-Slit Interference: Exploring Fringe Spacing

How far apart are the fringes on the screen?

When light of wavelength 490 nm in air shines on two slits 7.00×10^(-2) mm apart immersed in water with a refractive index of 1.33, and a viewing screen 60.0 cm away, the fringes on the screen are approximately how far apart?

The distance between the fringes on the screen is approximately 1.37 mm.

To calculate the fringe spacing, we can use the formula for the angular separation of fringes in a double-slit interference pattern:

θ = (m * λ) / (d * n)

where m is the order of the fringe, λ is the wavelength of the light, d is the distance between the slits, and n is the refractive index of the medium. We also need to consider the distance from the slits to the viewing screen (L) to find the fringe spacing on the screen:

y = L * tan(θ)

To find the fringe spacing, we can combine these formulas and calculate for m = 1:

y = L * tan((λ) / (d * n))

Plugging in the given values (λ = 490 nm, d = 7.00×10^(-2) mm, n = 1.33, and L = 60.0 cm), we get:

y ≈ 1.37 mm

In summary, when light of wavelength 490 nm in air shines on two slits 7.00×10^(-2) mm apart immersed in water with a refractive index of 1.33, and a viewing screen 60.0 cm away, the fringes on the screen are approximately 1.37 mm apart.