In a Young's double-slit experiment, the slits are 0.4mm apart and are illuminated by laser light of wavelength 602.4nm. The screen is 3.1m away. What is the number of dark fringes per centimetre?
To determine the number of dark fringes per centimeter, we need to first calculate the fringe separation, also known as fringe width.
The fringe width, denoted as β (beta), can be calculated using the formula:
β = λL / d
where:
λ is the wavelength of light in meters,
L is the distance from the slits to the screen in meters, and
d is the spacing between the two slits in meters.
Let's convert the given values to SI units:
λ = 602.4nm = 602.4 × 10^(-9) m
L = 3.1m
d = 0.4mm = 0.4 × 10^(-3) m
Now, let's substitute these values into the formula to find β:
β = (602.4 × 10^(-9) m) × (3.1 m) / (0.4 × 10^(-3) m)
β = 4.6552 × 10^(-3) m
Next, to calculate the number of dark fringes per centimeter, we'll use the formula:
Number of dark fringes per centimeter = 1 / β
Number of dark fringes per centimeter = 1 / (4.6552 × 10^(-3) m)
Calculating this value gives:
Number of dark fringes per centimeter ≈ 214.92
Therefore, there are approximately 214.92 dark fringes per centimeter in the Young's double-slit experiment with the given parameters.