In an experiment on young's double - slit with the light of wavele...
Given Information:
- Wavelength of light used in the experiment: 800 nm
- Distance between the slits: 2 mm = 0.002 m
- Initial distance between the screen and the slits: 1 m
- Final distance between the screen and the slits: 1.25 m
Explanation:
1. Fringe Width Formula:
The formula for calculating the fringe width in Young's double-slit experiment is given by:
β = λD / dWhere:
- β is the fringe width
- λ is the wavelength of light
- D is the distance between the screen and the slits
- d is the distance between the slits
2. Finding the Initial Fringe Width:
Using the given values, we can calculate the initial fringe width using the formula:
β
initial = λ
initial * D
initial / d
Substituting the given values:
β
initial = (800 * 10
-9) * 1 / 0.002
Simplifying the expression:
β
initial = 0.4 mm
3. Finding the Final Wavelength:
To find the new wavelength of light, we need to keep the fringe width constant when the screen is moved to a new distance.
Using the same formula, we can calculate the new wavelength as follows:
β
final = λ
final * D
final / d
Substituting the given values:
0.4 mm = λ
final * 1.25 / 0.002
Simplifying the expression:
λ
final = (0.4 mm * 0.002) / 1.25
Converting millimeters to meters and simplifying further:
λ
final = 0.00064 m = 640 nm
Therefore, the new wavelength of light should be 640 nm in order to maintain the same fringe width when the screen is moved to a distance of 1.25 m.