In Young's experiment, two coherent sources are placed 0.90 mm apart and fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the c... In Young's experiment, two coherent sources are placed 0.90 mm apart and fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, what would be the wavelength of the monochromatic light used?
Understand the Problem
The question is asking for the calculation of the wavelength of monochromatic light used in Young's double-slit experiment based on the given distances and the fringe patterns observed. We will use the formula for dark fringes in Young's experiment to solve this, which relates the distance between the slits, the distance to the screen, the position of the dark fringe, and the wavelength.
Answer
The wavelength $\lambda$ is calculated using the formula: $$ \lambda = \frac{y_m \cdot d}{(m + \frac{1}{2}) \cdot D} $$ The actual numerical answer will depend on the specific values provided for $y_m$, $d$, $D$, and $m$.
Answer for screen readers
The wavelength of the monochromatic light $\lambda$ can be calculated using the formula:
$$ \lambda = \frac{y_m \cdot d}{(m + \frac{1}{2}) \cdot D} $$
(The specific answer will depend on the provided variable values.)
Steps to Solve
-
Identify given variables
We are given the following values:
- $d$: distance between the slits (in meters)
- $D$: distance from the slits to the screen (in meters)
- $y_m$: position of the m-th dark fringe on the screen (in meters)
We will need to identify which specific values are provided to proceed.
-
Use the formula for dark fringes
In Young's experiment, the position of the m-th dark fringe is given by the formula:
$$ y_m = \frac{(m + \frac{1}{2}) \cdot \lambda \cdot D}{d} $$
Where $\lambda$ is the wavelength we are solving for. -
Rearrange the equation for wavelength
To find the wavelength $\lambda$, we can rearrange the formula:
$$ \lambda = \frac{y_m \cdot d}{(m + \frac{1}{2}) \cdot D} $$
This arrangement will allow us to substitute the known values easily. -
Substitute values and calculate
Now we will substitute the values for $y_m$, $d$, $D$, and $m$ into the rearranged equation to calculate $\lambda$. Ensure all dimensions are correctly accounted for when plugging in the values. -
Final calculation
Calculate the values to find the wavelength $\lambda$. Ensure the units are consistent (typically in meters).
The wavelength of the monochromatic light $\lambda$ can be calculated using the formula:
$$ \lambda = \frac{y_m \cdot d}{(m + \frac{1}{2}) \cdot D} $$
(The specific answer will depend on the provided variable values.)
More Information
In Young's double-slit experiment, the interference pattern produced allows us to determine the wavelength of light used based on the distances and fringe positions. This principle underlies many applications in physics, especially in wave theory.
Tips
- Forgetting to convert units: Always ensure that all measurements are in the same unit system (e.g., meters).
- Incorrectly substituting values into the formula: Check each value to ensure it corresponds correctly to the right variable in the formula.
- Not adjusting for the fringe order $m$: Remember that $m$ for dark fringes starts at 0.
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