How far apart are the fringes on the screen?
The fringes on the screen are approximately 3.96 mm apart when light of wavelength 440 nm in air falls on two slits 5.00x10⁻² mm apart and the slits are immersed in water. This involves the phenomenon of interference in light waves. The fringe separation is calculated using the formula for double-slit interference given by the equation:
y = Lλ/d.
Initially, let's convert everything into the same units. The wavelength (λ) is given as 440 nm or 4.4 x 10⁻⁷ m, the separation of the slits (d) is 5.00 x 10⁻² mm or 5 x 10⁻⁵ m, and the distance from the slits to the screen (L) is 45.0 cm or 0.45 m. Now, simply substitute these values into the equation:
y = (0.45 m)*(4.4 x 10⁻⁷ m)/(5 x 10⁻⁵ m).
When you do the calculations, the fringe separation y is found to be approximately 3.96 x 10⁻³ m or 3.96 mm.
In conclusion, the fringes on the screen are approximately 3.96 mm apart.
Calculating Fringe Separation
The phenomenon of double-slit interference in light waves occurs when light passes through two closely spaced slits and the resulting interference pattern is observed on a screen. In this case, light of wavelength 440 nm in air falls on two slits 5.00x10⁻² mm apart, and the slits are immersed in water. The question asks for the distance between the observed fringes on the screen. This distance is known as the fringe separation and can be calculated using the formula y = Lλ/d, where y is the fringe separation, L is the distance from the slits to the screen, λ is the wavelength of light, and d is the separation of the slits.
To start the calculation, we need to ensure that all values are in the same unit. The wavelength of light in air is given as 440 nm, which is equivalent to 4.4 x 10⁻⁷ m. The separation of the slits is provided as 5.00x10⁻² mm, which is equal to 5 x 10⁻⁵ m. The distance from the slits to the screen is given as 45.0 cm, which is equal to 0.45 m.
Substitute these values into the formula y = (0.45 m)*(4.4 x 10⁻⁷ m)/(5 x 10⁻⁵ m) and perform the calculations. The resulting fringe separation y is approximately 3.96 x 10⁻³ m or 3.96 mm. This means that the fringes on the screen are approximately 3.96 mm apart when light of wavelength 440 nm in air falls on two slits 5.00x10⁻² mm apart and the slits are immersed in water.
In conclusion, the calculation of fringe separation in double-slit interference provides valuable insights into the behavior of light waves and the phenomenon of interference. Understanding these principles can lead to further exploration and application of wave optics in various scientific and technological fields.