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1) $(theta_i,theta_r$,normale alla sup.) $in$ (stesso piano $pi$)

2) $theta_i=theta_r$

$n=c/v$

1) $(theta_i,theta_r$,normale alla sup.)$in$ (stesso piano $pi$)

2) $n_1sintheta_1=n_2sintheta_2$

$1/(f) =1/p + 1/q$

$G=-q/p$

Immagini virtuali $->$ q<0

Lente divergente $->$ f<0

Costruzione: 1) parallelo asse ottico poi per fuoco
2) per centro lente

$l=l_0(1+lambdaDeltat)$

$S=S_0(1+2lambdaDeltat)$

$V=l_0(1+3lambdaDeltat)$

$DeltaQ=c cdot m cdotDeltaT= CDeltaT$

Al=900; Ag=232; Au=128;; Cu=380;Fe=440; Hg=140; Pb=129;Sn=228 ;

Al=25E-6; Au=14E-6;Fe=12E-6; Ottone=20E-6; Platino=9E-6

Al=933K; Au=1234K;Fe=1808K; Ottone=1200K; Piombo=35K

$vecv_m=(Deltavecs)/(Deltat)$

$veca_m=(Deltavecv)/(Deltat)$

$vecv=lim_(Deltatrarr0)(Deltavecs)/(Deltat)$

$veca=lim_(Deltatrarr0)(Deltavecv)/(Deltat)$

$vecs=1/2 veca t^2 + vec v t + vec s_0$

$vecv=vec(v_0)+veca*t$

$s_("frenata")=v_("iniz")^2/(2a)

${(hatx","haty","hatz), (|hatx|=|haty|=|hatz|=1), (hat(hatx haty)=hat(haty hatz)=hat(hatz hatx)=90°),(hat(haty hatx)=hat(hatz haty)=hat(hatx hatz)=-90°) :}$

$P_x,P_y,P_z$

$kvecP=k({:(P_x),(P_y),(P_z) :})=({:(kP_x),(kP_y),(kP_z) :})$

$vecacdotvecb=abcos(theta)=a_xb_x+a_yb_y+a_zbz=Sigma_(i=1)^(i=3)a_ib_i=a^ib_i$

${(|vecatimesvecb|=absin(theta)=|a_xb_y-a_yb_x|), ("direzione dito medio mano dx") :}$

$[cos(alpha)=0.3] harr [alpha=cos^(-1)(0.3)]$

$[sin(alpha)=-0.7] harr [alpha=sin^(-1)(-0.7)]$

$[tan(alpha)=12] harr [alpha=tan^(-1)(12)]$

(S.R.I.)

${(vecx=vecx'+vec(v_t)), (vecv=vecv'+vec(v_t)), (veca=veca'), (vecF=vecF') :}$

${([vecv="costante"]harr[vecF=0]), (veca=(vecF)/(m_("inerz"))), (vecF_(12)=-vecF_(21)) :}$

${(F_(_|_)=P cos(alpha)), (F_("//")=P sin(alpha)):}$

$[F_("att.max.statico")=k_s*Nt]rarr[F_s<=k_s*N]$

$F_d=k_d*N$

$K=1/2 m v^2$

$U=m g h$

$E=1/2 k x^2$

$vecM=vecrtimesvecF$

$[vecomega="costante"]harr[vecM=0]$

${([vecomega="costante"]harr[vecM=0]), ([vecv="costante"]harr[vecR=0]) :}$

$vecomega_m=(vec(Deltatheta))/(Deltat)$

$vecalpha_m=(vec(Deltaomega))/(Deltat)$

$vecomega=lim_(Deltatrarr0)(vec(Deltatheta))/(Deltat)$

$vecalpha=lim_(Deltatrarr0)(vec(Deltaomega))/(Deltat)$

$vectheta=1/2 vecalpha t^2 + vec omega t + vec omega_0$

$vecomega=vec(omega_0)+vecalpha*t$

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E$=vBlsin(theta)$

E$=-(DeltaPhi(B))/(Deltat)$

$M=(Phi_("sec")(B_("prim")))/(I_("prim"))$

E_sec$=-(DeltaPhi(B_("prim")))/(Deltat)=-(Delta(DeltaMI_("prim")))/(Deltat)=-M(DeltaI_("prim"))/(Deltat)$

$L=(Phi(B)_("prim"))/(I_("prim"))$

E$=-(DeltaPhi(B))/(Deltat)=-((DeltaLI))/(Deltat)=-L(DeltaI)/(Deltat)$

$L_("sol")=(Phi_("sol")(B_("sol")))/(I_("sol"))=(NB_("sol")A)/i=(N·Nmu_0i/(l)A)/i=(N^2mu_0A)/l$

$En(B_("sol"))=1/2Li^2$

$u(B_("sol"))=1/(2mu)B^2$

${(Phi(vecE)=Q_("tot")/epsilon),(Gamma_(gamma)(vecE)=0),(Phi(vecB)=0),(Gamma_(gamma)(vecB)=muSigma_iI_i):}$

${(Phi(vecE)=Q_("tot")/epsilon),(Gamma_(gamma)(vecE)=(DeltaPhi(vecB))/(Deltat)),(Phi(vecB)=0),(Gamma_(gamma)(vecB)=mu(Sigma_iI_i+epsilon(DeltaPhi(vecE))/(Deltat))) :}$

$v=1/sqrt(epsilon mu)rarr[c=1/sqrt(epsilon_0 mu_0)=3·10^(8) m/s]$

$lambda=c/f$

$u_("elmw")=u(E)+u(B)=1/2epsilon_0E^2+1/(2mu_0)B^2$
$[u(E)=u(B)]
$[1/2epsilon_0E^2=1/(2mu_0)B^2]rarr[E^2=1/(mu_0epsilon_0)B^2]rarr[E=cB]$
$u_("elmw")(E)=epsilon_0E^2$
$u_("elmw")(B)=1/(mu_0)B^2$

$S=A·c·u=A·c·$

$vecP=epsilon_0(vecE xx vecB)$
$p=epsilon_0E E/csin90°=(epsilon_0E^2)/c=u/c

$f_r=f_s(1pmv_r/c)$

$p=F/A=((Deltaq)/(Deltat))/A=((PAcDeltat)/(Deltat))/(A)=Pc=u/c c =u$

$[Deltaq=2Deltaq]rarrp=2u$

$p=ucostheta$

$p=2ucostheta$

$p=u/3$

$p=2u/3$

$barS=barS_0cos^2theta$

$beta=v/c$

$gamma(beta)=1/sqrt(1-beta^2)$

$Deltat=gammaDeltat_0$

$L=L_0/gamma$

$m=gammam_0$

$vecp=mvecv=gammam_0vecv$

$E_0=m_0c^2$

$E_("tot")=gammam_0c^2$

$K=E_("tot")-E_0=gammam_0c^2-m_0c^2=m_0c^2(gamma-1)$

$[E_("tot")(p)=E=gammam_0c^2=gammam_0(v/v)c^2=(gammam_0v)(c^2/v)=(pc^2)/v]$
$E=(pc^2)/vrarr(beta)=v/c=(pc)/E$
$E=(mc^2)/(sqrt(1-beta^2))=(mc^2)/(sqrt(1-(p^2c^2)/E^2)$
$E^2=(m^2c^4)/((E^2-p^2c^2)/E^2)
$E^2=E^2((m^2c^4)/(E^2-p^2c^2))$
$1=(m^2c^4)/(E^2-p^2c^2)$
$E^2-p^2c^2=m^2c^4$
$E_("tot")(p)=m^2c^4+p^2c^2$

$v=(v_1+v_2)/(1+(v_1v_2)/c^2)$

$sigma=5.67·10^(-8)J/(s·m^2·K^4)$
$E=sigmaT^4$

$E_(Planck)=nhf$
h=6.63·10^(-34)J·s

$E=hf$

$K_(max)=hf-W_0$

$p_(gamma)=E_(gamma)/c=(hf)/c=h/(c/f)=h/lambda_(gamma) rarr lambda_(gamma)=h/p_(gamma)$

$lambda_(prt,"De Broglie")=h/p_(prt)$

$lambda_("Compton",e)=h/p_(e)=h/(m_ec)=2.43$pm

$lambda'=lambda+h/(mc)(1-costheta)$

$(Δp_x)·(Δx)≥barh/2$

$(ΔE)·(Δt)≥barh/2$

(Lyman,Balmer,Paschen)
$m=1,2,3,R=1.097·10^7m^(-1)$
$1/lambda=R(1/m^2-1/n^2)$

$hf=E_i-E_f$

$L_n=nbarh$

$r_n=(5.29·10^(-11)m)n^2/Z$

$E_n=(13.6 eV)n^2/Z$