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
Step 1: Identify the given values and the relevant formulas. The given values are: Object height, h_o = 4.0 cm Object distance, u = 8.3 cm Focal length of the concave mirror, f = 15.2 cm We need to find the image distance (v) and the image size (h_i). The mirror formula is: (1)/(f) = (1)/(u) + (1)/(v) The magnification formula is: M = (h_i)/(h_o) = -(v)/(u) For a concave mirror, the focal length f is positive. The object distance u is positive for a real object. Step 2: Calculate the image distance (v). Rearrange the mirror formula to solve for v: (1)/(v) = (1)/(f) - (1)/(u) Substitute the given values: (1)/(v) = (1)/(15.2 cm) - (1)/(8.3 cm) (1)/(v) = 0.065789 cm^-1 - 0.120482 cm^-1 (1)/(v) = -0.054693 cm^-1 v = (1)/(-0.054693 cm)^-1 v ≈ -18.28 cm The negative sign indicates that the image is virtual and formed behind the mirror. Step 3: Calculate the image size (h_i). Use the magnification formula: (h_i)/(h_o) = -(v)/(u) Rearrange to solve for h_i: h_i = -h_o ((v)/(u)) Substitute the known values: h_i = -(4.0 cm) (-18.28 cm8.3 cm) h_i = (4.0 cm) ((18.28)/(8.3)) h_i = (4.0 cm) × 2.2024 h_i ≈ 8.81 cm The positive sign indicates that the image is upright. The image distance is -18.3 cm and the image size is 8.81 cm. Send me the next one 📸