Logo

AskSia

Plus

29题怎么做 Q28. The cladding of a step-Index optical fibre A reduces material disper...
May 20, 2024
29题怎么做
Answer
The fringe spacing ww is 0.84 mm
Solution
a
To determine the fringe spacing ww, we need to measure the distance between the dark fringes in Figure 2. Since there are 10 dark fringes, the distance between the first and the last dark fringe is measured and divided by 9 (the number of spaces between 10 fringes). If the total distance is 7.56 mm, then w=7.56 mm9=0.84 mmw = \frac{7.56 \, \text{mm}}{9} = 0.84 \, \text{mm}
Key Concept
Fringe spacing in Young's double-slit experiment
Explanation
The fringe spacing ww is the distance between adjacent dark or bright fringes in an interference pattern. It can be calculated by measuring the total distance covered by a number of fringes and dividing by the number of spaces between them.
29b
Answer
The percentage uncertainty in the value for the fringe spacing ww is calculated.
Solution
a
Measure the fringe spacing ww: Measure the distance between several dark fringes in Figure 2 and divide by the number of fringes to find the average fringe spacing ww
b
Determine the absolute uncertainty: Estimate the uncertainty in the measurement of the distance between fringes. This could be due to the precision of the measuring instrument or human error
c
Calculate the percentage uncertainty: Use the formula for percentage uncertainty: Percentage Uncertainty=(Absolute UncertaintyMeasured Value)×100 \text{Percentage Uncertainty} = \left( \frac{\text{Absolute Uncertainty}}{\text{Measured Value}} \right) \times 100 Substitute the values for the absolute uncertainty and the measured fringe spacing ww into the formula
Key Concept
Percentage Uncertainty
Explanation
The percentage uncertainty is a way to express the uncertainty of a measurement as a percentage of the measured value. It is calculated by dividing the absolute uncertainty by the measured value and multiplying by 100.
29c
Sure, Starryblue! Let's go through the steps to calculate the wavelength of the laser light using Young's double-slit method. Given: - Distance between the slits and the screen, DD - Fringe spacing, xx - Distance between the slits, dd - Uncertainties in the measurements
Answer
The wavelength of the laser light is calculated using the formula λ=xdD\lambda = \frac{xd}{D}.
Solution
a
Formula for Wavelength: The wavelength λ\lambda of the laser light can be calculated using the formula λ=xdD\lambda = \frac{xd}{D}, where xx is the fringe spacing, dd is the distance between the slits, and DD is the distance from the slits to the screen
b
Substitute Values: Substitute the given values into the formula. For example, if x=0.5 mmx = 0.5 \, \text{mm}, d=0.2 mmd = 0.2 \, \text{mm}, and D=1 mD = 1 \, \text{m}, then λ=0.5×10−3×0.2×10−31=1×10−7 m=100 nm\lambda = \frac{0.5 \times 10^{-3} \times 0.2 \times 10^{-3}}{1} = 1 \times 10^{-7} \, \text{m} = 100 \, \text{nm}
c
Calculate Uncertainty: To find the uncertainty in λ\lambda, use the formula for propagation of uncertainties. If Δx\Delta x, Δd\Delta d, and ΔD\Delta D are the uncertainties in xx, dd, and DD respectively, then the uncertainty in λ\lambda is given by: Δλ=λ(Δxx)2+(Δdd)2+(ΔDD)2 \Delta \lambda = \lambda \sqrt{\left(\frac{\Delta x}{x}\right)^2 + \left(\frac{\Delta d}{d}\right)^2 + \left(\frac{\Delta D}{D}\right)^2} Substitute the values to find Δλ\Delta \lambda
Key Concept
Wavelength Calculation Using Young's Double-Slit Experiment
Explanation
The wavelength of the laser light can be determined using the fringe spacing, the distance between the slits, and the distance from the slits to the screen. The formula λ=xdD\lambda = \frac{xd}{D} is used, and uncertainties are calculated using propagation of uncertainties.
所以wavelength是多少？
Answer
The wavelength of the laser light is determined using the formula λ=xdL\lambda = \frac{xd}{L}
Solution
a
Measure the fringe spacing (x): The fringe spacing is the distance between adjacent bright or dark fringes on the screen. Let's denote this as xx
b
Measure the distance between the slits (d): The distance between the two slits in the double-slit apparatus is denoted as dd
c
Measure the distance from the slits to the screen (L): The distance from the slits to the screen where the fringes are observed is denoted as LL
d
Calculate the wavelength (λ\lambda): Use the formula λ=xdL\lambda = \frac{xd}{L} to calculate the wavelength of the laser light
Key Concept
Young's double-slit experiment
Explanation
The wavelength of light can be determined using the fringe spacing, the distance between the slits, and the distance from the slits to the screen in Young's double-slit experiment.
具体数字放进去啊
Solution
a
To calculate the percentage uncertainty in ww, use the formula: Percentage uncertainty=(Uncertainty in ww)×100 \text{Percentage uncertainty} = \left( \frac{\text{Uncertainty in } w}{w} \right) \times 100 If the uncertainty in ww is given as Δw\Delta w and the value of ww is given, substitute these values into the formula
# (c) Calculate the wavelength of the laser light.
a
Use the formula for the wavelength λ\lambda in Young's double-slit experiment: λ=w⋅dL \lambda = \frac{w \cdot d}{L} where ww is the fringe spacing, dd is the distance between the slits, and LL is the distance from the slits to the screen. Substitute the given values: d=0.420 mm=0.420×10−3 m,L=8.40 m d = 0.420 \, \text{mm} = 0.420 \times 10^{-3} \, \text{m}, \quad L = 8.40 \, \text{m} Calculate λ\lambda in nm: λ=w⋅0.420×10−38.40×109 nm \lambda = \frac{w \cdot 0.420 \times 10^{-3}}{8.40} \times 10^9 \, \text{nm}
# (d) Calculate the absolute uncertainty in your value for the wavelength.
a
To find the absolute uncertainty in λ\lambda, use the percentage uncertainties in dd and LL: Percentage uncertainty in λ=(Δdd)2+(ΔLL)2+(Δww)2 \text{Percentage uncertainty in } \lambda = \sqrt{\left( \frac{\Delta d}{d} \right)^2 + \left( \frac{\Delta L}{L} \right)^2 + \left( \frac{\Delta w}{w} \right)^2} Given: Δdd=1.2%,ΔLL=0.6%,Δww=(from part b) \frac{\Delta d}{d} = 1.2\%, \quad \frac{\Delta L}{L} = 0.6\%, \quad \frac{\Delta w}{w} = \text{(from part b)} Calculate the total percentage uncertainty and then the absolute uncertainty: Absolute uncertainty=(Percentage uncertainty in λ)×λ \text{Absolute uncertainty} = \left( \text{Percentage uncertainty in } \lambda \right) \times \lambda
Question 30 # (a) Calculate the wavelength of the light used to produce the interference pattern.
a
Use the formula for the wavelength λ\lambda in Young's double-slit experiment: λ=w⋅dL \lambda = \frac{w \cdot d}{L} where ww is the fringe spacing, dd is the distance between the slits, and LL is the distance from the slits to the screen. Substitute the given values: d=0.25 mm=0.25×10−3 m,w=7.8 mm=7.8×10−3 m,L=3.5 m d = 0.25 \, \text{mm} = 0.25 \times 10^{-3} \, \text{m}, \quad w = 7.8 \, \text{mm} = 7.8 \times 10^{-3} \, \text{m}, \quad L = 3.5 \, \text{m} Calculate λ\lambda: λ=7.8×10−3⋅0.25×10−33.5×109 nm \lambda = \frac{7.8 \times 10^{-3} \cdot 0.25 \times 10^{-3}}{3.5} \times 10^9 \, \text{nm}
29 Answer
The percentage uncertainty in ww, the wavelength of the laser light, and the absolute uncertainty in the wavelength are calculated as described.
30 Answer
The wavelength of the light used to produce the interference pattern is calculated as described.
Key Concept
Young's double-slit experiment and the calculation of wavelength and uncertainties.
Explanation
The wavelength of light in Young's double-slit experiment can be determined using the fringe spacing, slit separation, and distance to the screen. Uncertainties in measurements propagate to the final result.
What is the formula to calculate the wavelength of light in an interference pattern using the separation of the two sources and the fringe separation?
Answer
The formula to calculate the wavelength of light in an interference pattern using the separation of the two sources and the fringe separation is λ=xdLλ = \frac{xd}{L}
Solution
a
Formula Definition: The formula λ=xdLλ = \frac{xd}{L} is used to calculate the wavelength of light in an interference pattern. Here, λλ represents the wavelength of the light, xx is the fringe separation (distance between adjacent bright or dark fringes), dd is the separation between the two sources (slits), and LL is the distance from the slits to the screen where the pattern is observed
b
Application: To use this formula, measure the fringe separation xx, the distance between the slits dd, and the distance from the slits to the screen LL. Substitute these values into the formula to find the wavelength λλ
Key Concept
Interference Pattern Wavelength Calculation
Explanation
The formula λ=xdLλ = \frac{xd}{L} allows us to determine the wavelength of light by measuring the fringe separation, the distance between the slits, and the distance to the screen. This relationship is derived from the principles of wave interference and diffraction.
© 2023 AskSia.AI all rights reserved