Question

Printr-o lama cu fete plan-paralele cu sticla,cu indicele n1=1,5 care se gaseste intr-un mediu transparent cu indice de refractie n0=1(aer) se refracta o raza de lumina alba. Aflati care este distanta d dintre care raza incidenta si raza emergenta,masurata pe o perpendiculara coborata si punctul de emergenta.

Answer 1

$\Delta ABC:sin(i-r)=\frac{BC}{AB} =>BC=ABsin(i-r)\\\Delta ADB:cosr=\frac{x}{AB} =>AB=\frac{x}{cosr} \\BC=ABsin(i-r)=\frac{x}{cosr}sin(i-r)\\sin^2r+cos^2r=1=>cosr=\sqrt{1-sin^2r}\\n_osini=n_1sinr=>sinr=\frac{n_osini}{n_1}\\ cosr=\sqrt{1-\frac{n_0^2sin^2i}{n_1^2} } =\sqrt{\frac{n_1^2-n_o^2sin^2i}{n_1^2} }$

$BC=x\frac{(sini*cosr-cosi*sinr)}{cosr} =x(sini-\frac{n_osini*cosi}{n_1\sqrt{\frac{n_1^2-n_o^2sin^2i}{n_1^2} }}=xsini(1-\frac{\sqrt{1-n_o^2sin^2i} }{\sqrt{n_1^2-n_o^2sin^2i} })$