what is the angle between the first order and the second order bright fringes for a yellow light with a wave length of 605 nm, and a distance between two slits of 0.0550 mm?
Use the formula you find here:
http://en.wikipedia.org/wiki/Double-slit_experiment
0.63
To calculate the angle between the first order and second order bright fringes for a given set of parameters, we can use the formula for the fringe separation obtained from the double-slit interference:
λ = (x * d) / D
where:
λ = wavelength of light
x = fringe separation (distance between bright fringes)
d = distance between the slits
D = distance from the double slit to the screen
Let's plug in the given values to calculate the fringe separation:
λ = 605 nm = 605 * 10^(-9) m (convert to meters)
d = 0.0550 mm = 0.0550 * 10^(-3) m (convert to meters)
Let's assume the distance from the double slit to the screen (D) is a large distance, which makes the angles small. In that case, the small-angle approximation can be used:
θ = x / D (small-angle approximation)
Now we can rearrange the first equation to solve for x:
x = λ * D / d
Finally, we can substitute the values into the equation to find the fringe separation:
x = (605 * 10^(-9) m) * D / (0.0550 * 10^(-3) m)
x = (605 * 10^(-9)) * (D / 0.0550) m
Now you can use this equation to find the fringe separation x.
Please note that to find the specific angles between the fringes, you would need to know the value of D (distance from the double slit to the screen). Without that information, we can only provide the formula to calculate the fringe separation.
To find the angle between the first order and second order bright fringes for a double-slit interference pattern, you can use the formula:
\( \theta = \frac{m \lambda}{d} \)
Where:
- \( \theta \) is the angle between the bright fringes
- \( m \) is the order of the fringe (first order, second order, etc.)
- \( \lambda \) is the wavelength of the light
- \( d \) is the distance between the two slits
For your specific example, the given values are:
- \( \lambda = 605 \) nm (or \( \lambda = 605 \times 10^{-9} \) m)
- \( d = 0.0550 \) mm (or \( d = 0.0550 \times 10^{-3} \) m)
First, convert the given values to SI units:
- \( \lambda = 605 \times 10^{-9} \) m
- \( d = 0.0550 \times 10^{-3} \) m
For the first order bright fringe (\( m = 1 \)):
\( \theta_1 = \frac{1 \times \lambda}{d} \)
Substituting the given values:
\( \theta_1 = \frac{1 \times 605 \times 10^{-9} \, \text{m}}{0.0550 \times 10^{-3} \, \text{m}} \)
Now, calculate the value of \( \theta_1 \) using a calculator. The result will be in radians.
For the second order bright fringe (\( m = 2 \)):
\( \theta_2 = \frac{2 \times \lambda}{d} \)
Substituting the given values:
\( \theta_2 = \frac{2 \times 605 \times 10^{-9} \, \text{m}}{0.0550 \times 10^{-3} \, \text{m}} \)
Again, calculate the value of \( \theta_2 \) using a calculator.
The angle between the first order and second order bright fringes is the difference between \( \theta_2 \) and \( \theta_1 \). Subtract \( \theta_1 \) from \( \theta_2 \) to find the result.
Note: If the result is in radians but you want it in degrees, you can use the conversion factor: 1 radian = 180/π degrees.