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A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is (are) true?

Options

  1. AThe refractive index of the lens is 2.5
  2. BThe radius of curvature of the convex surface is 45 cm
  3. CThe faint image is erect and real
  4. DThe focal length of the lens is 20 cm.

Correct answer

A. The refractive index of the lens is 2.5

Step-by-step solution

1 v - 1 u = 1 f 1 60 - 1 - 30 = 1 f ⇒ f = 20 c m ...(i) Also 1 f = n - 1 1 R - 1 ∞ = n - 1 R ....(ii) For reflection from convex mirror (curved surface) 1 v + 1 u = 1 f = 2 R ....(iii) R = 30 cm From (i), (ii) and (iii) n = 2.5 , Faint image erect and virtual

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