If the x-coordinate of the position of a particle is known to an accuracy of $\delta x$, then the x-component of momentum cannot be determined to an accuracy better than $\Delta P_{x}\approx \frac{\hbar }{\Delta x}$.
$\Delta P_{x}. \Delta x\approx \hbar$
The above inequality must be satisfied
$\Delta P_{x}. \Delta x\geqslant \hbar$
Where $\hbar $ - Planck’s Constant
This is the Uncertainty principle with macroscopic objects.
Exact statement of the Uncertainty principle →
The product of the uncertainties in determining the position and momentum of the particle can never be smaller than the number of the order $\frac{\hbar }{2}$.
$\Delta P_{x}. \Delta x\geqslant \frac{\hbar}{2}$
Where $\delta x$ and $\delta P $ are defined as the root mean square deviation from their mean values.
The Uncertainty principle can also describe by the following formula →
$\Delta x.\Delta p_{x}\approx \frac{\hbar}{2}$
$\Delta x.\Delta p_{x}\geqslant \frac{\hbar}{2}$
$\Delta x.\Delta p_{x}\geqslant \frac{h}{4\pi }$
Expression for $y$ and $z$ component →
$\Delta y.\Delta p_{y}\geqslant \frac{h}{4\pi }$
$\Delta z.\Delta p_{z}\geqslant \frac{h}{4\pi }$
The uncertainty relation between energy and time →
$\Delta E.\Delta t\geqslant \frac{h}{4\pi }$
$\Delta E.\Delta t\geqslant \frac{\hbar }{2 }$
The uncertainty relation between momentum and Angular Position→
$\Delta L.\Delta \theta \geqslant \frac{h }{4\pi }$
$\Delta L.\Delta \theta \geqslant \frac{\hbar}{2}$
Angle of Acceptance → If incident angle of light on the core for which the incident angle on the core-cladding interface equals the critical angle then incident angle of light on the core is called the "Angle of Acceptance. Transmission of light when the incident angle is equal to the acceptance angle If the incident angle is greater than the acceptance angle i.e. $\theta_{i}>\theta_{0}$ then the angle of incidence on the core-cladding interface will be less than the critical angle due to which part of the incident light is transmitted into cladding as shown in the figure below Transmission of light when the incident angle is greater than the acceptance angle If the incident angle is less than the acceptance angle i.e. $\theta_{i}<\theta_{0}$ then the angle of incidence on the core-cladding interface will be greater than the critical angle for which total internal reflection takes place inside the core. As shown in the figure below Transmission of lig
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