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A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x', to the nearest integer, is ______.
Correct answer is '600'. Can you explain this answer?
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A fringe width of 6 mm was produced for two slits separated by 1 mm ap...
Understanding Fringe Width in Double-Slit Experiment
The fringe width in a double-slit experiment can be calculated using the formula:
Fringe Width (β) = (λ * D) / d
where:
- λ = wavelength of light
- D = distance from slits to screen
- d = distance between the slits
Given Values
- Fringe width (β) = 6 mm = 6 x 10^-3 m
- Distance between slits (d) = 1 mm = 1 x 10^-3 m
- Distance from slits to screen (D) = 10 m
Rearranging the Formula
To find the wavelength (λ), we can rearrange the formula:
λ = (β * d) / D
Substituting the Values
Now, substitute the known values into the rearranged formula:
- β = 6 x 10^-3 m
- d = 1 x 10^-3 m
- D = 10 m
Calculation Steps
1. Plug in the values:
λ = (6 x 10^-3 m * 1 x 10^-3 m) / 10 m
2. Calculate:
λ = (6 x 10^-6 m) / 10
λ = 6 x 10^-7 m
3. Convert to nanometers:
λ = 6 x 10^-7 m = 600 nm
Conclusion
Thus, the wavelength of light used in this experiment is approximately 600 nm, confirming the correct answer.
The fringe width in a double-slit experiment can be calculated using the formula:
Fringe Width (β) = (λ * D) / d
where:
- λ = wavelength of light
- D = distance from slits to screen
- d = distance between the slits
Given Values
- Fringe width (β) = 6 mm = 6 x 10^-3 m
- Distance between slits (d) = 1 mm = 1 x 10^-3 m
- Distance from slits to screen (D) = 10 m
Rearranging the Formula
To find the wavelength (λ), we can rearrange the formula:
λ = (β * d) / D
Substituting the Values
Now, substitute the known values into the rearranged formula:
- β = 6 x 10^-3 m
- d = 1 x 10^-3 m
- D = 10 m
Calculation Steps
1. Plug in the values:
λ = (6 x 10^-3 m * 1 x 10^-3 m) / 10 m
2. Calculate:
λ = (6 x 10^-6 m) / 10
λ = 6 x 10^-7 m
3. Convert to nanometers:
λ = 6 x 10^-7 m = 600 nm
Conclusion
Thus, the wavelength of light used in this experiment is approximately 600 nm, confirming the correct answer.
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Community Answer
A fringe width of 6 mm was produced for two slits separated by 1 mm ap...
λ = 6 × 10-7 m = 600 × 10-9 m
λ = 600 nm
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A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is x nm. The value of x, to the nearest integer, is ______.Correct answer is '600'. Can you explain this answer?
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