Monochromatic light falls on two narrow slits that are 0.0190 mm apart. A first order fringe is 18 mm from the central line. The screen (back wall) is 0.600 m from the slits. What is the wavelength of the light?
We can use the equation for the fringe separation in a double-slit experiment to solve this problem:
$$y = m \frac{\lambda L}{s}$$
Here, y is the first order fringe distance from the central line, m is the order number, λ is the wavelength of the light, L is the distance between the slits and the screen, and s is the distance between the slits. Rearranging the equation to solve for λ, we get:
$$\lambda = \frac{y s}{m L}$$
Plugging in the given values, we can calculate the wavelength:
$$\lambda = \frac{18 \times 10^{-3}\,\text{m} \times 0.0190 \times 10^{-3}\,\text{m}}{1 \times 0.600\,\text{m}}$$
$$\lambda = \frac{3.42 \times 10^{-7}\,\text{m}^2}{0.600\,\text{m}}$$
$$\lambda = 5.7 \times 10^{-7}\,\text{m}$$
The wavelength of the light is approximately 570 nm.
Well, if we're talking about narrow slits, I hope they're not the kind you wear on your pants! Anyway, let's get to your question.
To find the wavelength of the light, we can use Young's double-slit equation:
wavelength = (distance to the screen * slit separation) / fringe separation
Plugging in the values, we have:
wavelength = (0.600 m * 0.0190 mm) / 18 mm
First, let's convert the millimeter values to meters:
wavelength = (0.600 m * 0.0000190 m) / 0.018 m
Now, we can do some math:
wavelength = 0.0000114 / 0.018
And finally:
wavelength = 0.000633 m
So, it looks like the wavelength of the light is approximately 0.000633 meters. Don't ask me to make any fashion statements with that!
To find the wavelength of the light, we can use the equation:
λ = (m * d) / L
Where:
λ is the wavelength of the light,
m is the order of the fringe,
d is the distance between the slits, and
L is the distance from the slits to the screen.
Given:
d = 0.0190 mm = 0.0190 * 10^(-3) m
m = 1 (first order fringe)
L = 0.600 m
Substituting the values into the equation:
λ = (1 * 0.0190 * 10^(-3)) / 0.600
Calculating:
λ = (0.0190 * 10^(-3)) / 0.600
= 0.0317 * 10^(-3) m
Therefore, the wavelength of the light is 0.0317 * 10^(-3) m.
To find the wavelength of the light, we can use the equation for the location of the fringe:
y = m * λ * L / d
Where:
y = distance from the central line to the fringe
m = order of the fringe (in this case, m = 1 for the first-order fringe)
λ = wavelength of the light
L = distance between the slits and the screen (in this case, L = 0.600 m)
d = distance between the two slits (d = 0.0190 mm = 0.0190 x 10^-3 m)
Plugging in the values, we can rearrange the equation to solve for λ:
λ = y * d / (m * L)
Substituting the given values:
y = 18 mm = 18 x 10^-3 m (convert to meters)
m = 1
L = 0.600 m
d = 0.0190 x 10^-3 m
λ = (18 x 10^-3 m) * (0.0190 x 10^-3 m) / (1 * 0.600 m)
Simplifying the equation, we get:
λ = 0.018 / 0.600
Calculating the value, we find:
λ ≈ 0.03 x 10^-3 m
Therefore, the wavelength of the monochromatic light is approximately 0.03 x 10^-3 meters.