Final answer:
L₁ is a convex lens with a focal length of 10 cm, L₂ is a convex lens with a focal length of 20 cm, and L₃ is a concave lens with a focal length of -10 cm. L₂ (Convex, 20 cm) is the one that will form a virtual and magnified image of an object placed at 15 cm from the lens.
Step-by-step explanation:
The lenses L₁, L₂, and L₃ have powers of +10 D, +5 D, and -10 D respectively. The power of a lens is the reciprocal of its focal length in meters, P = 1/f, where f is the focal length and P is the power in diopters. Therefore, we can calculate the focal lengths by taking the reciprocal of the power for each lens.
- L₁: Convex lens with power +10 D, focal length is f₁ = 1/10 m = 10 cm.
- L₂: Convex lens with power +5 D, focal length is f₂ = 1/5 m = 20 cm.
- L₃: Concave lens with power -10 D, focal length is f₃ = -1/10 m = -10 cm. (Note the negative sign indicates a diverging lens).
The correct answer here is a) L₁: Convex, 10 cm; L₂: Convex, 20 cm; L₃: Concave, -10 cm. To determine which lens will form a virtual and magnified image, we need to consider the object distance and the type of lens. A convex lens forms a virtual image when the object is placed within its focal length, while a concave lens always forms a virtual image.
Since the object is placed at 15 cm from the lens, L₁ will not form a virtual image because its focal length is 10 cm and the object is placed beyond this focal point. L₂, however, has a focal length of 20 cm and hence will form a virtual and magnified image because the object is within its focal length. Lens L₃ will form a virtual image, but it will be diminished and not magnified.