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You have three lenses L₁, L₂, and L₃ of power +10 D, +5 D, and -10 D respectively. State the nature and focal length of each lens. Explain which of the three lenses will form a Virtual and magnified image of an object placed at 15 cm from the lens.

a) L₁: Convex, 10 cm; L₂: Convex, 5 cm; L₃: Concave, 10 cm
b) L₁: Convex, 10 cm; L₂: Concave, 5 cm; L₃: Convex, 10 cm
c) L₁: Concave, 10 cm; L₂: Convex, 5 cm; L₃: Concave, 10 cm
d) L₁: Concave, 10 cm; L₂: Concave, 5 cm; L₃: Convex, 10 cm

User Diezsiete
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1 Answer

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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.

User Binncheol
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