Pregunta: Problem 3 (20 points)Calculate the percentage of light transmitted through two materials. Light enters material 1 from the air (8 = 0.3 cm1) and leaves the second material (B = 0.35 cm-1) into the air as well. It is known that the refractive index between the two materials is very similar (n = 1.5), as well as their thickness (l = 0.02 m). In

Problem $3(20$ points$)$

Calculate the percentage of light transmitted through two materials. Light enters material $1$ from the air $(8=0\mathrm{.}3$ cm$1)$ and leaves the second material $($B $=0\mathrm{.}35$ cm$-1)$ into the air as well. It is known that the refractive index between the two materials is very similar $($n $=1\mathrm{.}5),$ as well as their thickness $($l $=0\mathrm{.}02$ m$).$ In addition, a layer of an anti$-$reflective material is applied to material $1,$ which makes the reflection on the first material negligible.

Development $(5$ points$)$ per question$)$

a$)$ Explain the Meissner effect and name an application.

b$)$ As seen in class, it would be correct to assert that $"$As the temperature increases, the mobility of the charge carriers will decrease as a consequence of an increase in thermal energy resulting in increased vibration of the crystal lattices. It doesn't matter if they're metallic or semiconductor materials." Justify your answer.

$($c$)$ If light is transmitted from air to a thin sheet of polymethylmethacrylate, will the speed of Does the light increase or decrease?, explain.

d$)$ Indicate, either A or B$,$ the case in which Ephotons $<$ Eg$,$ using Figure $1$ as a reference.

Intensity

$($A$)$

$($B$)$

Figure $1.$ Intensity of light when interacting with a semiconductor material

e$)$ Calculate the probability of finding an electron with an energy higher than the Fermi energy at

Or K$.$ Use the following equation:Problema $3(20$ puntos$)$

Calcule el porcentaje de luz transmitido a trav$é$s de dos materiales. La luz entra al material $1$ desde el aire

$(\beta =0,3c{m}^{-1})$ y abandona el segundo material $(\beta =0,35c{m}^{-1})$ tambi$é$n hacia el aire. Se sabe que el $í$ndice

de refracci$ó$n entre ambos materiales es muy similar $(n=1,5),$ as$í$ como su espesor $(l=0,02m).$ Adem$á$s$,$

sobre el material $1$ se aplica una capa de un material antireflectivo que hace que la reflexi$ó$n en el primer

material sea despreciable.

Desarrollo $(5$ puntos por pregunta$)$

a$)$ Explique el efecto Meissner y mencione una aplicaci$ó$n$.$

b$)$ Seg$ú$n lo visto en clase, ser$í$a correcto asegurar que $"$Al aumentar la temperatura, la movilidad de los

portadores de carga disminuir$á$ como consecuencia de un aumento en la energ$í$a t$é$rmica que resulta

en una mayor vibraci$ó$n de las redes cristalina. Sin importar si son materiales met$á$licos o

semiconductores". Justifique su respuesta.

c$)$ Si se transmite luz desde aire a una l$á$mina fina de polimetilmetacrilate, cla velocidad de la luz

aumenta o disminuye?, explique.

d$)$ Indique, ya sea $A$@$B,$ el rasn on ol nu$юf(E)=\frac{1}{e^{\frac{(E-E_F)}{k_{B}T}}+1}\sigma =n|e|{\mu }_e+p|e|{\mu }_h$

$E=hv=\frac{hc}{\lambda }$

$n=\frac{c}{v}=\frac{\sqrt[\phantom{2}]{\epsilon lon\mu }}{\sqrt[\phantom{2}]{\epsilon lo{n}_0{\mu }_0}}=\sqrt[\phantom{2}]{\epsilon lo{n}_r{\mu }_r}$

$\sigma ={\sigma }_0{e}^{-\frac{E_g}{2}{k}_{B}T}$

$\sigma ={\sigma }_0{e}^{-\frac{E_a-E_d}{k_B}T}$

$\sigma ={\sigma }_0{e}^{-\frac{E_a}{k_B}T}$

$R=(\frac{n_2-n_1}{n_2+n_1}{)}^2$

$I=I_0{e}^{-\beta l}$

$\sigma =n|e|{\mu }_e$

${\mu }_r=\frac{\mu }{{\mu }_0}$

$B={\mu }_{0}H+{\mu }_{0}M$

$B=\mu H$

$M={\chi }_{m}H$

${\mu }_B=9,27\times {10}^{-24}A{m}^{2}F=\frac{{\mu }_0{M}^{2}A}{2}{F}_{\text{d}\text{o}\text{t}\text{s}\text{.}\text{d}\text{o}\text{t}\text{s}\text{d}\text{o}\text{t}\text{s}\text{d}\text{o}\text{t}\text{s}}.$ usando $la$ figura $1$ como referencia.

Figura $1.$ Intensidad $(intensity)dela$ luz $al$ interactuar con $un$ material semiconductor

$e$