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 given values and determine the focal length. The object distance is u = 30 cm. The radius of curvature of the concave mirror is R = 20 cm. For a concave mirror, the focal length f is half the radius of curvature and is negative according to the Cartesian sign convention. f = -(R)/(2) f = -20 cm2 f = -10 cm According to the Cartesian sign convention, for a real object placed in front of the mirror, the object distance u is negative. u = -30 cm Step 2: Calculate the image position (v) using the mirror formula. The mirror formula is: (1)/(f) = (1)/(v) + (1)/(u) Substitute the values of f and u: (1)/(-10 cm) = (1)/(v) + (1)/(-30 cm) Rearrange the formula to solve for v: (1)/(v) = (1)/(-10 cm) - (1)/(-30 cm) (1)/(v) = -(1)/(10 cm) + (1)/(30 cm) To combine the fractions, find a common denominator, which is 30: (1)/(v) = (-3)/(30 cm) + (1)/(30 cm) (1)/(v) = (-3 + 1)/(30 cm) (1)/(v) = (-2)/(30 cm) (1)/(v) = -(1)/(15 cm) v = -15 cm i) The position The image is formed 15 cm in front of the mirror. v = -15 cm Step 3: Determine the nature of the image. The negative sign of v indicates that the image is formed on the same side as the object (in front of the mirror). Images formed in front of a mirror are real. For a real image formed by a mirror, it is always inverted. ii) The nature The image is Real and Inverted. Step 4: Calculate the magnification (M). The magnification formula is: M = -(v)/(u) Substitute the values of v and u: M = --15 cm-30 cm M = -(15)/(30) M = -(1)/(2) M = -0.5 The negative sign of M confirms that the image is inverted. The magnitude |M| = 0.5 indicates that the image is diminished (smaller than the object). iii) Magnification M = -0.5