Light falls on a double slit with slit separation
of 2.19 × 10
−6 m, and the first bright fringe is
seen at an angle of 12.7
◦
relative to the central
maximum.
What is the wavelength of the light?
Answer in units of nm
Can the person post the steps and equations.
To find the wavelength of light in this scenario, you can use the double-slit interference formula. Here are the steps to solve the problem:
Step 1: Convert the angle from degrees to radians.
The formula requires the angle to be in radians, so let's convert 12.7 degrees to radians.
Angle in radians = (12.7 degrees) x (π radians/180 degrees)
= 0.221 radians (approximately)
Step 2: Calculate the distance between the slits.
Given the slit separation of 2.19 × 10^(-6) m.
Step 3: Use the double-slit interference formula.
The formula is: λ = (d * sin(θ)) / m
where:
λ = wavelength of light
d = distance between the slits
θ = angle of the first bright fringe (converted to radians)
m = order of the fringe (which is 1 for the first bright fringe)
Plug in the values:
λ = (2.19 × 10^(-6) m * sin(0.221)) / 1
Step 4: Convert the result to nanometers.
The formula gives the wavelength of light in meters, but the answer is requested in nanometers.
1 nm = 1 × 10^(-9) m
Multiply the value by 1 × 10^9 to convert it to nanometers.
λ (in nm) = λ (in m) * 1 × 10^9
Now you can calculate the final answer by plugging in the values and performing the calculations.
Please note that the formula assumes that the angle is measured from the center of the central maximum to the first bright fringe. If the angle is measured differently, the formula may change slightly.