To solve this problem it is necessary to apply the concepts related to the concept of overlap and constructive interference.
For this purpose we have that the constructive interference in waves can be expressed under the function
![a sin\theta = m\lambda](https://tex.z-dn.net/?f=a%20sin%5Ctheta%20%3D%20m%5Clambda)
Where
a = Width of the slit
d = Distance of slit to screen
m = Number of order which represent the number of repetition of the spectrum
Angle between incident rays and scatter planes
At the same time the distance on the screen from the central point, would be
![sin\theta = \frac{y}{d}](https://tex.z-dn.net/?f=sin%5Ctheta%20%3D%20%5Cfrac%7By%7D%7Bd%7D)
Where y = Represents the distance on the screen from the central point
PART A ) From the previous equation if we arrange to find the angle we have that
![\theta = sin^{-1}(\frac{y}{d})](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20sin%5E%7B-1%7D%28%5Cfrac%7By%7D%7Bd%7D%29)
![\theta = sin^{-1}(\frac{1.4*10^{-2}}{3})](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20sin%5E%7B-1%7D%28%5Cfrac%7B1.4%2A10%5E%7B-2%7D%7D%7B3%7D%29)
![\theta = 0.2673\°](https://tex.z-dn.net/?f=%5Ctheta%20%3D%200.2673%5C%C2%B0)
PART B) Equation both equations we have
![a sin\theta = m\lambda](https://tex.z-dn.net/?f=a%20sin%5Ctheta%20%3D%20m%5Clambda)
![a \frac{y}{d} = m\lambda](https://tex.z-dn.net/?f=a%20%5Cfrac%7By%7D%7Bd%7D%20%3D%20m%5Clambda)
Re-arrange to find a,
![a = \frac{(2)(385*10^{-9})(3)}{(1.4*10^{-2})}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%282%29%28385%2A10%5E%7B-9%7D%29%283%29%7D%7B%281.4%2A10%5E%7B-2%7D%29%7D)
![a = 1.65*10^{-4}m](https://tex.z-dn.net/?f=a%20%3D%201.65%2A10%5E%7B-4%7Dm)
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Answer:
2.64N
Explanation:
Force = mass * acceleration
Given
mass = 4kg
distance = 1.9m
Time t = 2.4s
Get the acceleration using the equation of motion
S = ut + 1/2at²
1.9 = 0 + 1/2a(2.4)²
1.9 = 5.76a/2
1.9 = 2.88a
a = 1.9/2.88
a = 0.66m/s²
Get the magnitude of the force
Force = 4 * 0.66
Force = 2.64N
Hence the net force acting on the fish is 2.64N