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 formula for a convex mirror. Given: Object distance, u = 12 cm Focal length of convex mirror, f = -15 cm (focal length is negative for convex mirrors) Object height, h_o = 4.5 cm The mirror formula is: (1)/(f) = (1)/(v) + (1)/(u) where v is the image distance. 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 cm) - (1)/(12 cm) Find a common denominator, which is 60: (1)/(v) = (-4)/(60 cm) - (5)/(60 cm) (1)/(v) = (-4 - 5)/(60 cm) (1)/(v) = (-9)/(60 cm) v = 60 cm-9 v = -(20)/(3) cm ≈ -6.67 cm The negative sign for v indicates that the image is formed behind the mirror, meaning it is a virtual image. Step 3: Calculate the magnification (M). The magnification formula is: M = -(v)/(u) Substitute the values of v and u: M = -(-20)/(3) cm12 cm M = (20)/(3 × 12) M = (20)/(36) M = (5)/(9) ≈ 0.56 The positive sign for M indicates that the image is upright. Step 4: Calculate the size (height) of the image (h_i). The magnification formula also relates image height (h_i) to object height (h_o): M = (h_i)/(h_o) Rearrange to solve for h_i: h_i = M × h_o Substitute the values of M and h_o: h_i = (5)/(9) × 4.5 cm h_i = (5)/(9) × (9)/(2) cm h_i = (5)/(2) cm h_i = 2.5 cm Step 5: Summarize the image characteristics. • Location: The image is located (20)/(3) cm or approximately 6.67 cm behind the mirror. • Size: The image height is 2.5 cm. • Nature: The image is virtual and upright. • Magnification: The magnification is (5)/(9) or approximately 0.56. Final Answer: The location of the image is 6.67 cm behind the mirror. The size of the image is 2.5 cm. The nature of the image is virtual and upright. The magnification of the image is 0.56. Send me the next one 📸