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A point object O is placed on the principal axis of a convex lens of focal length 20 cm at a distance of 40cm to the left of it. The diameter of the lens is 10 cm. If the eye is placed 60 cm to the right of the lens at a distance h below the principal axis, then the maximum value of h to see the image will be
  • a)
    0
  • b)
    5 cm
  • c)
    2.5 cm
  • d)
    10 cm
Correct answer is option 'C'. Can you explain this answer?
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A point object O is placed on the principal axis of a convex lens of f...
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A point object O is placed on the principal axis of a convex lens of f...
Explanation:

  • Given, focal length of convex lens, f = 20cm

  • Distance of object from lens, u = -40cm (negative sign indicates object is placed to the left of lens)

  • Diameter of lens, D = 10cm

  • Distance of eye from lens, v = 60cm

  • Maximum value of h is to be found



Formula:

  • 1/f = 1/v - 1/u

  • magnification (m) = v/u

  • Height of image (h') = h/m



Calculation:

  • Using lens formula, we can find the distance of image from lens:


    • 1/f = 1/v - 1/u

    • 1/20 = 1/v + 1/40

    • v = 40cm


  • Using magnification formula, we can find the magnification produced by the lens:


    • m = v/u = 40/-40 = -1


  • Since the magnification is negative, the image is inverted

  • The height of the object is (D/2) = 5cm

  • Using the formula for height of image:


    • h' = h/m = -h


  • Since h' is positive, h must be negative, implying that the image is below the principal axis

  • Maximum value of h can be found by assuming that the image is at the farthest possible distance from the lens:


    • v' = infinity

    • 1/f = 1/v' - 1/u

    • 1/20 = 0 - 1/40'

    • 40' = infinity


  • Therefore, the image is formed at infinity, and the maximum value of h is half the diameter of the lens:


    • h = D/2 = 5cm




Therefore, the correct answer is option C) 2.5cm.
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A point object O is placed on the principal axis of a convex lens of focal length 20 cm at a distance of 40cm to the left of it. The diameter of the lens is 10 cm. If the eye is placed 60 cm to the right of the lens at a distance h below the principal axis, then the maximum value of h to see the image will bea)0 b)5 cmc) 2.5 cmd)10 cmCorrect answer is option 'C'. Can you explain this answer?
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