Question

La ce departare de o lentila convergenta cu f=20 cm trebuie asezat un obiect pentru a obtine o imagine de 4 ori mai mare ca obiectul. Caracterizati imaginea.

Answer 1

   
Notatii:

x₁ = distanta dintre obiect si lentila
x₂ = distanta dintre lentila si imagine
f   = distanta focala = 20 cm
h₁ = inaltimea obiectului
h₂ = inaltimea imaginii

[tex]\displaystyle\bf\\ \text{Folosim formulele:}\\\\ \frac{1}{x_1}+\frac{1}{x_2}=\frac{1}{f}\\\\ \frac{h_1}{h_2}= \frac{x_1}{x_2}\\\\ Rezolvare:\\\\ h_2 ~\text{ este de 4 ori mai mare decat }~h_1\\\\ \frac{h_1}{h_2}=\frac{1}{4}\\\\ \frac{h_1}{h_2}=\frac{x_1}{x_2}=\frac{1}{4}\\\\ \boxed{\bf x_2=4x_1}\\\\\\ \frac{1}{x_1}+\frac{1}{x_2}=\frac{1}{f}\\\\ \frac{1}{x_1}+\frac{1}{4x_1}=\frac{1}{20}\\\\ \frac{4}{4x_1}+\frac{1}{4x_1}=\frac{1}{20}\\\\ \frac{4+1}{4x_1}=\frac{1}{20}[/tex]


[tex]\displaystyle\bf\\ \frac{5}{4x_1}=\frac{1}{20}\\\\ 4x_1 = 20 \cdot 5\\\\ x_1 = \frac{20 \cdot 5}{4} = \frac{100}{4} = \boxed{\bf25~cm}~~\text{(distanta de la obiect la lentila)}[/tex]