This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Huu hapa ni utatuzi wa swali la 5: 5. An object 5cm high is placed 20cm in front of a converging lens of focal length 15cm. Find the power of the lens and the magnification of the lens. Tunapewa: Urefu wa kitu, h_o = 5 cm Umbali wa kitu, u = 20 cm Urefu wa focal, f = 15 cm (kwa lenzi inayokusanya, f ni chanya) Step 1: Tafuta Nguvu ya Lenzi (Power of the lens) Nguvu ya lenzi (P) inatolewa na fomula P = (1)/(f), ambapo f lazima iwe katika mita. Kwanza, badilisha urefu wa focal kutoka sentimita kwenda mita: f = 15 cm = 0.15 m Sasa, hesabu nguvu ya lenzi: P = (1)/(0.15 m) P = (100)/(15) D P = (20)/(3) D P ≈ 6.67 D Nguvu ya lenzi ni 6.67 D Step 2: Tafuta Umbali wa Picha (v) kwa kutumia Fomula ya Lenzi Fomula ya lenzi ni: (1)/(f) = (1)/(v) - (1)/(u) Tuna f = 15 cm na u = 20 cm. Badilisha maadili haya kwenye fomula: (1)/(15) = (1)/(v) - (1)/(20) Tenga (1)/(v): (1)/(v) = (1)/(15) + (1)/(20) Tafuta kigawe cha kawaida cha 15 na 20, ambacho ni 60: (1)/(v) = (4)/(60) + (3)/(60) (1)/(v) = (7)/(60) v = (60)/(7) cm v ≈ 8.57 cm Step 3: Tafuta Ukuzaji wa Lenzi (Magnification of the lens) Ukuzaji (M) unatolewa na fomula: M = -(v)/(u) Tuna v = (60)/(7) cm na u = 20 cm. Badilisha maadili haya kwenye fomula: M = -(60)/(7)20 M = -(60)/(7 × 20) M = -(3)/(7) M ≈ -0.43 Ukuzaji wa lenzi ni -0.43 Last free one today — make it count tomorrow, or type /upgrade for unlimited.