Final answer:
In Young's double-slit experiment, the first dark fringe is observed directly opposite to one of the slits. The wavelength of light can be calculated using the formula wavelength = slit separation * (screen distance / path difference). Plugging in the given values, the wavelength of light is 80 nm.
Step-by-step explanation:
In Young's double-slit experiment, the first dark fringe is observed directly opposite to one of the slits. This occurs when the path difference between the two waves from the slits is equal to half the wavelength of light.
In the given scenario, the distance between the slits is 0.6 mm and the distance from the slits to the screen is 80 cm. The first dark fringe is directly opposite to one of the slits, so the path difference is equal to the separation between the slits, which is 0.6 mm.
Using the formula for path difference, path difference = slit separation * (screen distance / wavelength), we can rearrange the formula to solve for the wavelength of light:
wavelength = slit separation * (screen distance / path difference)
Plugging in the values, we get:
wavelength = 0.6 mm * (80 cm / 0.6 mm) = 80 cm
Therefore, the wavelength of light will be 80 nm.