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Three lenses L₁, L₂ , and L₃ are placed coaxially in that order. The focal lengths of L₁ and L₃ are +20 cm and +15 cm respectively. The distance between L₁ and L₂ is 10 cm , and the distance between L₂ and L₃ is 25 cm . A point object is placed on the principal axis at a distance of 60 cm in front of L₁ . If the emergent rays from L₃ are parallel to the principal axis, the focal length of lens L₂ is :

Options

  1. A15 cm
  2. B20 cm
  3. C-40 cm
  4. D20 3 cm

Correct answer

B. 20 cm

Step-by-step solution

For lens L₁ , applying the thin lens formula: 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -60 = 1 20 1 v₁ = 1 20 - 1 60 = 2 60 v₁ = +30 cm The image formed by L₁ is 30 cm to its right. Since L₂ is 10 cm from L₁ , this image acts as a virtual object for L₂ at a distance: u₂ = +(30 - 10) = +20 cm For lens L₃ , the emergent rays are parallel to the principal axis, meaning its image is at infinity ( v₃ = ). 1 - 1 u₃ = 1 15 u₃ = -15 cm The object for L₃ is the image formed by L₂ . Since L₂ and L₃ are separated by 25 cm , the image dist

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