A double-slit interference experiment is performed with light from a laser. The separation between the slits is 0.58 mm, and the
first-order maximum of the interference pattern is at an angle of 0.060
◦
from the center of
the pattern.
What is the wavelength of the laser light?
Answer in units of nm
The coordinate of the maximum is
x(max) = k•λ•L/d,
for the first max k=1
x(max1) = λ•L/d,
tanα = x(max1)/L = λ/d.
λ = d• tanα = 0.55•10^-3•1.047•10^-3 = 5.76•10^-7 = 576 nm
Excuse me what was the equation you used? Because the answer is wrong.
And where did you get those numbers?
I've taken 0.55 mm instead of 0.58 mm
If d = 0.55•10^-3, and tan α =1.047•10^-3,
λ = d• tanα = 0.58•10^-3•1.047•10^-3 = 6.07•10^-7 = 607 nm.
To find the wavelength of the laser light, we can use the formula for the double-slit interference pattern:
λ = (d * sin(θ)) / m
Where:
λ is the wavelength of the light
d is the separation between the slits (in meters)
θ is the angle from the center of the pattern (in radians)
m is the order of the maximum
First, let's convert the given values to the required units:
d = 0.58 mm = 0.58 * 10^(-3) m (convert millimeters to meters)
θ = 0.060 degrees = 0.060 * π/180 radians (convert degrees to radians)
m = 1 (first-order maximum)
Now, we can plug in these values into the formula to find the wavelength:
λ = (0.58 * 10^(-3) * sin(0.060 * π/180)) / 1
Calculating this expression, we can find the wavelength of the laser light.