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
Q:12 A concave lens has focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also find the magnification of the lens. Step 1: Identify the given values and apply sign conventions. For a concave lens: • Focal length (f) is negative. So, f = -15 cm. • The image formed by a concave lens is always virtual and on the same side as the object. So, the image distance (v) is negative. v = -10 cm. Step 2: Calculate the object distance (u) using the lens formula. The lens formula is: (1)/(f) = (1)/(v) + (1)/(u) Rearrange the formula to solve for (1)/(u): (1)/(u) = (1)/(f) - (1)/(v) Substitute the values: (1)/(u) = (1)/(-15 cm) - (1)/(-10 cm) (1)/(u) = -(1)/(15 cm) + (1)/(10 cm) Find a common denominator, which is 30: (1)/(u) = -(2)/(30 cm) + (3)/(30 cm) (1)/(u) = (1)/(30 cm) u = 30 cm Step 3: Calculate the magnification (M) of the lens. The magnification formula is: M = -(v)/(u) Substitute the values: M = --10 cm30 cm M = (10)/(30) M = (1)/(3) M ≈ 0.33 The object should be placed at a distance of 30 cm from the lens. The magnification of the lens is 0.33.