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What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

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1. Given Data

Using the standard sign convention for lenses:

  • Focal length of Convex Lens (f1): +30 cm
  • Focal length of Concave Lens (f2): -20 cm

2. Calculation of Equivalent Focal Length

The formula for the effective focal length (F) of two lenses in contact is:

1/F = 1/f1 + 1/f2

Substituting the values:

  • 1/F = 1/30 + 1/(-20)
  • 1/F = 1/30 - 1/20

Taking the LCM of 30 and 20 (which is 60):

  • 1/F = (2 - 3) / 60
  • 1/F = -1 / 60

Inverting both sides:

Equivalent Focal Length (F) = -60 cm

3. Nature of the System

The sign of the effective focal length determines the nature of the lens system:

  • Positive (+): Converging (Convex behavior)
  • Negative (-): Diverging (Concave behavior)

Final Conclusion

  • Focal Length: 60 cm
  • Nature: Since the focal length is negative (-60 cm), the system behaves as a Diverging Lens.

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