Snell's law

Derivation from Fermat's principle[edit]

Snell's law can be derived from Fermat's principle, which states that the light travels the path which takes the least time. By taking the derivative of the optical path length, the stationary point is found giving the path taken by the light (though the result does not show light taking the least time path, but rather one that is stationary with respect to small variations as there are cases where light actually takes the greatest time path, as in a spherical mirror). In a classic analogy, the area of lower refractive index is replaced by a beach, the area of higher refractive index by the sea, and the fastest way for a rescuer on the beach to get to a drowning person in the sea is to run along a path that follows Snell's law.

Light from medium 1, point Q, enters medium 2, refraction occurs, and reaches point P finally.

As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are ${\displaystyle n_{1}}$ and ${\displaystyle n_{2}}$ respectively. Light enters medium 2 from medium 1 via point O.

${\displaystyle \theta _{1}}$ is the angle of incidence, ${\displaystyle \theta _{2}}$ is the angle of refraction.

The traveling velocities of light in medium 1 and medium 2 are

${\displaystyle v_{1}=c/n_{1}}$ and

${\displaystyle v_{2}=c/n_{2}}$ respectively.

${\displaystyle c}$ is the speed of light in vacuum.

Let T be the time required for the light to travel from point Q to point P.

${\displaystyle T={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+(l-x)^{2}}}{v_{2}}}={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+l^{2}-2lx+x^{2}}}{v_{2}}}}$

To minimize it, one can differentiate :

${\displaystyle {\frac {dT}{dx}}={\frac {x}{v_{1}{\sqrt {x^{2}+a^{2}}}}}+{\frac {-(l-x)}{v_{2}{\sqrt {(l-x)^{2}+b^{2}}}}}=0}$ (stationary point)

Note that ${\displaystyle {\frac {x}{\sqrt {x^{2}+a^{2}}}}=\sin \theta _{1}}$

and ${\displaystyle {\frac {l-x}{\sqrt {(l-x)^{2}+b^{2}}}}=\sin \theta _{2}}$

Therefore,

${\displaystyle {\frac {dT}{dx}}={\frac {\sin \theta _{1}}{v_{1}}}-{\frac {\sin \theta _{2}}{v_{2}}}=0}$

${\displaystyle {\frac {\sin \theta _{1}}{v_{1}}}={\frac {\sin \theta _{2}}{v_{2}}}}$

${\displaystyle {\frac {n_{1}\sin \theta _{1}}{c}}={\frac {n_{2}\sin \theta _{2}}{c}}}$

${\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}$

15.Impact and Non-Impact printer

Printers
Impact and Non-Impact Printers are two categories of the printer. Impact printers
involve mechanical components for conducting printing. While in Non-Impact printers,
no mechanical moving component is used.

Impact Printers:
It is a type of printer that works by direct contact of an ink ribbon with paper. These
printers are typically loud but remain in use today because of their unique ability to
function with multi part forms. An impact printer has mechanisms resembling those of
a typewriter.
Example of Impact Printers, Dot-matrix printers, Daisy-wheel printers, and line printers.

Non-Impact Printers:
It is a type of printer that does not hit or impact a ribbon to print. They used laser,
xerographic, electrostatic, chemical and ink jet technologies. Non-impact printers are
generally much quieter. They are less likely to need maintenance or repairs than earlier
impact printers.
Example of Non-Impact Printers is Ink jet printers and Laser printers.