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
Here are the solutions to the pinhole camera problems: 1) Step 1: Convert all units to meters. Object distance (u) = 10\, cm = 0.1\, m Object height (H_o) = 5\, m Image distance (v) = 2\, m Step 2: Calculate the height of the image (H_i) using the magnification formula. (H_i)/(H_o) = (v)/(u) H_i = H_o × (v)/(u) H_i = 5\, m × 2\, m0.1\, m H_i = 5\, m × 20 = 100\, m Step 3: Calculate the magnification (M). M = (v)/(u) M = 2\, m0.1\, m = 20 2) Step 1: Identify the given values and convert units. Image distance (v) = 12.67\, m Screen height (H_screen) = 16\, cm = 0.16\, m Object height (H_o) = 1.86\, m For a full photo, the image height (H_i) must be equal to the screen height. So, H_i = 0.16\, m. Step 2: Calculate the maximum object distance (u) using the magnification formula. (H_i)/(H_o) = (v)/(u) u = v × (H_o)/(H_i) u = 12.67\, m × 1.86\, m0.16\, m u = 12.67\, m × 11.625 u = 147.3\, m 3) Step 1: Convert all units to meters. Object height (H_o) = 3.0\, m Object distance (u) = 7.50\, m Image height (H_i) = 8.00\, cm = 0.08\, m Step 2: Calculate the distance of the film from the pinhole (image distance, v) using the magnification formula. (H_i)/(H_o) = (v)/(u) v = u × (H_i)/(H_o) v = 7.50\, m × 0.08\, m3.0\, m v = 7.50\, m × 0.02666... v = 0.20\, m 4) Step 1: Convert all units to meters. Screen side = 160\, mm = 0.16\, m Image distance (v) = 150\, mm = 0.15\, m Object distance (u) = 11\, m The image occupies three quarters of the height of the screen, so image height (H_i) = (3)/(4) × 0.16\, m = 0.12\, m. Step 2: Calculate the height of the flag staff (object height, H_o) using the magnification formula. (H_i)/(H_o) = (v)/(u) H_o = H_i × (u)/(v) H_o = 0.12\, m × 11\, m0.15\, m H_o = 0.12\, m × 73.333... H_o = 8.8\, m 5) Step 1: Identify the given values. Length of pinhole camera (image distance, v) = 0.1\, m Object height (H_o) = 1\, m Object distance (u) = 2\, m Step 2: Calculate the height of the image (H_i) using the magnification formula. (H_i)/(H_o) = (v)/(u) H_i = H_o × (v)/(u) H_i = 1\, m × 0.1\, m2\, m H_i = 1\, m × 0.05 H_i = 0.05\, m 3 done, 2 left today. You're making progress.