Two thin slits with separation of .0250mm are placed over monochromatic orange laser light at 610.nm. What is the small angle measurement from the central maximum (zero degrees, inline with the source) to the first maximum?
I thought in order to solve this is would be sin^-1(y/D) but all I got was a domain error on my calculator. So how am I supposed to solve this?
so many views so little answers :(
To solve this problem, you can use the concept of interference in the case of double-slit diffraction. The condition for constructive interference (maximum intensity) for the double-slit interference pattern is given by the equation:
d * sin(θ) = m * λ
Where:
- d is the distance between the slits (given as 0.0250 mm),
- λ is the wavelength of light (given as 610 nm or 610 × 10^-9 m),
- θ is the angle between the central maximum and the first-order maximum (which you need to find),
- m is the order of the interference (you are looking for the angle to the first maximum, so m = 1).
To find the angle, you need to rearrange the equation and solve for sin(θ):
sin(θ) = (m * λ) / d
Plugging in the values, you get:
sin(θ) = (1 * 610 × 10^-9 m) / 0.0250 × 10^-3 m
Taking the inverse sine (sin^-1) of both sides will give you the value of the angle θ. However, you encountered a domain error on your calculator because the angle is very small.
In order to resolve this issue, make sure your calculator is set to radians mode instead of degrees mode, as the angle in this case will be in radians. Alternatively, you can convert the calculation to degrees by using the conversion factor (180°/π radians).
So, using either mode, calculate the following:
θ = sin^-1((1 * 610 × 10^-9) / (0.0250 × 10^-3))
Make sure your calculator is set correctly to either radians or degrees and enter the values correctly.