The indicated data are of clear understanding for the development of Airy's theory. In optics this phenomenon is described as an optical phenomenon in which The Light, due to its undulatory nature, tends to diffract when it passes through a circular opening.
The formula used for the radius of the Airy disk is given by,
![y_r=1.22\frac{\lambda f}{d}](https://tex.z-dn.net/?f=y_r%3D1.22%5Cfrac%7B%5Clambda%20f%7D%7Bd%7D)
Where,
Range of the radius
wavelength
f= focal length
Our values are given by,
State 1:
![d=2.00mm = 2*10^{-3}m](https://tex.z-dn.net/?f=d%3D2.00mm%20%3D%202%2A10%5E%7B-3%7Dm)
![f= 25mm = 25*10^{-3}m](https://tex.z-dn.net/?f=f%3D%2025mm%20%3D%2025%2A10%5E%7B-3%7Dm)
![\lambda = 750nm = 750*10^{-9}m](https://tex.z-dn.net/?f=%5Clambda%20%3D%20750nm%20%3D%20750%2A10%5E%7B-9%7Dm)
State 2:
![d=8.00mm = 8*10^{-3}m](https://tex.z-dn.net/?f=d%3D8.00mm%20%3D%208%2A10%5E%7B-3%7Dm)
![f= 25mm = 25*10^{-3}m](https://tex.z-dn.net/?f=f%3D%2025mm%20%3D%2025%2A10%5E%7B-3%7Dm)
![\lambda = 390nm = 390*10^{-9}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20390nm%20%3D%20390%2A10%5E%7B-9%7D)
Replacing in the first equation we have:
![y_{r1} = 1.22\frac{(750*10^{-9})(25*10^{-3})}{2*10^{-3}}](https://tex.z-dn.net/?f=y_%7Br1%7D%20%3D%201.22%5Cfrac%7B%28750%2A10%5E%7B-9%7D%29%2825%2A10%5E%7B-3%7D%29%7D%7B2%2A10%5E%7B-3%7D%7D)
![y_{r1}= 11.4\mu m](https://tex.z-dn.net/?f=y_%7Br1%7D%3D%2011.4%5Cmu%20m)
And also for,
![y_{r2} =1.22\frac{(390*10^{-9})(25*10^{-3})}{8*10^{-3}}](https://tex.z-dn.net/?f=y_%7Br2%7D%20%3D1.22%5Cfrac%7B%28390%2A10%5E%7B-9%7D%29%2825%2A10%5E%7B-3%7D%29%7D%7B8%2A10%5E%7B-3%7D%7D)
![y_{r2} = 1.49\mu m](https://tex.z-dn.net/?f=y_%7Br2%7D%20%3D%201.49%5Cmu%20m)
Therefor, the airy disk radius ranges from
to ![11.4\mu m](https://tex.z-dn.net/?f=11.4%5Cmu%20m)
We want to find how much momentum the dumbbell has at the moment it strikes the floor. Let's use this kinematics equation:
Vf² = Vi² + 2ad
Vf is the final velocity of the dumbbell, Vi is its initial velocity, a is its acceleration, and d is the height of its fall.
Given values:
Vi = 0m/s (dumbbell starts falling from rest)
a = 10m/s² (we'll treat downward motion as positive, this doesn't affect the result as long as we keep this in mind)
d = 80×10⁻²m
Plug in the values and solve for Vf:
Vf² = 2(10)(80×10⁻²)
Vf = ±4m/s
Reject the negative root.
Vf = 4m/s
The momentum of the dumbbell is given by:
p = mv
p is its momentum, m is its mass, and v is its velocity.
Given values:
m = 10kg
v = 4m/s (from previous calculation)
Plug in the values and solve for p:
p = 10(4)
p = 40kg×m/s
32 degrees Fahrenheit
And
0 degrees Celsius