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.
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You're on a roll — here's the solution for question 21: Given values: Object distance, u = 8 cm Focal length of converging lens, f = 6 cm a) Calculate the position of the image formed. Step 1: Use the lens formula. The lens formula for a thin lens is given by: (1)/(f) = (1)/(v) + (1)/(u) where f is the focal length, v is the image distance, and u is the object distance. For a converging lens, f is positive. For a real object, u is positive. (1)/(6 cm) = (1)/(v) + (1)/(8 cm) Step 2: Solve for the image distance v. (1)/(v) = (1)/(6 cm) - (1)/(8 cm) Find a common denominator, which is 24: (1)/(v) = (4)/(24 cm) - (3)/(24 cm) (1)/(v) = (1)/(24 cm) v = 24 cm The positive value of v indicates that the image is formed on the opposite side of the lens from the object. The position of the image formed is 24 cm from the lens, on the opposite side of the object. b) Give an application of this arrangement of a lens. When an object is placed between the focal point (f) and twice the focal length (2f) of a converging lens (here, f=6 cm, 2f=12 cm, and u=8 cm), a real, inverted, and magnified image is formed. This arrangement is used in devices that require a magnified real image. An application of this arrangement is a projector (e.g., slide projector or movie projector) or the objective lens of a compound microscope. c) Describe the nature of the image formed. Step 1: Determine if the image is real or virtual. Since the image distance v is positive (+24 cm), the image is formed by actual intersection of refracted rays, meaning it is a real image. Step 2: Determine if the image is upright or inverted. For a real image formed by a single converging lens, the image is always inverted. Step 3: Determine if the image is magnified or diminished. The magnification M is given by M = -(v)/(u). M = -24 cm8 cm = -3 The magnitude of magnification |M| = 3, which is greater than 1, indicating that the image is magnified. The nature of the image formed is real, inverted, and magnified. What's next? Send 'em!