A student doing Young's experiment measures a distance of 6.0 cm between the first and seventh nodal points on a screen located 3.0 m from the slit plate.
a) if the slit seperation is 220 x10 to the -6, what is the wave length of light being used ?
b) what colour is the light ?
x=2k•λ•L/2d= k•λ•L/d,
Δx=x7-x1 =
=7•λ•L/d - 1•λ•L/d = 6•λ•L/d,
λ = Δx•d/6•L =
=0.06•220•10^-6/6•3=
=7.3•10^-7 m .
Red light
To solve these questions, we will use the formula for the distance between nodal points and the wavelength of light in Young's experiment:
Distance between nodal points = (n * λ * D) / d
Where:
- n is the order of the nodal point (in this case, n = 7-1 = 6)
- λ is the wavelength of light
- D is the distance between the slit plate and the screen
- d is the separation between the slits
a) To find the wavelength of light being used, we rearrange the formula and solve for λ:
Distance between nodal points * d = n * λ * D
λ = (Distance between nodal points * d) / (n * D)
Using the given values:
Distance between nodal points = 6.0 cm = 0.06 m
d = 220 x 10^-6 m
n = 6
D = 3.0 m
λ = (0.06 m * 220 x 10^-6 m) / (6 * 3.0 m)
λ = 0.132 x 10^-6 m
λ = 1.32 x 10^-7 m
Therefore, the wavelength of light being used is 1.32 x 10^-7 m.
b) To determine the color of light, you can use the approximate wavelength ranges for different colors. Here are some common approximate wavelength ranges:
- Red: 620 nm - 750 nm
- Orange: 590 nm - 620 nm
- Yellow: 570 nm - 590 nm
- Green: 495 nm - 570 nm
- Blue: 450 nm - 495 nm
- Violet: 380 nm - 450 nm
Converting the wavelength we calculated to nanometers:
1.32 x 10^-7 m = 1.32 x 10^-7 m * 10^9 nm/m = 132 nm
Based on the approximate wavelength ranges, the light used in this experiment is violet.
To solve this problem, we can use the formula for the distance between the nodal points in Young's experiment:
d = (m * λ * L) / d
Where:
- d is the distance between the nodal points
- m is the order of the nodal points (in this case, m = 7-1 = 6)
- λ is the wavelength of light used
- L is the distance between the screen and the slit plate
Let's calculate the wavelength of light being used:
a) To find the wavelength (λ), rearrange the formula and solve for λ:
λ = (d * d) / (m * L)
Substituting the given values:
d = 6.0 cm = 0.06 m (convert to meters)
m = 6
L = 3.0 m
λ = (0.06 m * 0.06 m) / (6 * 3.0 m)
λ = 0.0036 m^2 / (18 m)
λ = 0.0002 m
Therefore, the wavelength of light being used is 0.0002 meters or 2.0 x 10^-4 meters.
b) To determine the color of light, we can use the relationship between wavelength and color. Different colors of light have different ranges of wavelengths. For visible light, the approximate ranges are:
- Red: 620 - 750 nm
- Orange: 590 - 620 nm
- Yellow: 570 - 590 nm
- Green: 495 - 570 nm
- Blue: 450 - 495 nm
- Violet: 380 - 450 nm
Converting the wavelength we found to nanometers:
λ = 2.0 x 10^-4 m = 200 nm
From the range of visible light, we can see that a wavelength of 200 nm falls in the violet color range. Therefore, the color of the light being used in this experiment can be determined to be violet.