Light shines through a single slit whose width is 1.12 mm. A diffraction pattern is formed on a screen located 4.0 m away. The distance between the middle central bright fringe and the second dark fringe is 4.0 mm. What is the wavelength of the light?
To find the wavelength of light in this scenario, we can use the formula for the distance between fringes in a single-slit diffraction pattern:
D * λ = d * L / w
where:
D is the distance between the bright fringe and the dark fringe (4.0 mm in this case),
λ is the wavelength of light (what we're trying to find),
d is the width of the slit (1.12 mm),
L is the distance from the slit to the screen (4.0 m), and
w is the distance from the center of the pattern to a particular fringe.
Rearranging the formula, we get:
λ = (d * L) / (D * w)
Plugging in the given values:
λ = (1.12 mm * 4.0 m) / (4.0 mm * 4.0 mm)
Simplifying:
λ = (0.00448 m) / (0.016 mm)
Converting mm to m:
λ = (0.00448 m) / (0.000016 m)
Simplifying further:
λ = 280 nm
Therefore, the wavelength of the light in this scenario is 280 nanometers (nm).