Focal length of combined glass lens and water lens

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SUMMARY

The discussion focuses on calculating the focal length of a combined glass lens and water lens system. The lens maker's formula was initially misapplied, leading to confusion regarding the focal length calculations. The correct approach involves recognizing the combination of two lenses: a glass lens with air on one side and water on the other, alongside a concave water lens. The solution manual clarifies that a thin layer of air is inserted between the lenses, allowing for the refractive index (n0) to be set to 1 for both lenses, resulting in accurate calculations.

PREREQUISITES
  • Understanding of the lens maker's formula
  • Knowledge of refractive indices, specifically for glass (1.5) and water (1.33)
  • Familiarity with the concept of combined lenses
  • Basic principles of optics, including curvature and focal length
NEXT STEPS
  • Study the application of the lens maker's formula in complex lens systems
  • Explore the effects of different refractive indices on lens performance
  • Investigate the principles of combining multiple lenses in optical systems
  • Learn about the impact of air gaps between lenses on focal length calculations
USEFUL FOR

Students studying optics, physics educators, and anyone involved in designing or analyzing optical systems with combined lenses.

desmond iking
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Homework Statement



please refer to the photo,

Homework Equations





The Attempt at a Solution


why can't I directly use the lens maker formula to get the ans ?
my working is 1/f = ( (1.5-1.33) /1.33) x ( (1/20) + 0 ) ...finally , i get my f = -160cm.
the radius of curvature of glass is 0
 

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Strange, I get +160 cm using the lens maker formula as you write it.
That would be for a glass lens fully submerged in water (the 1.33 for n0)

But the exercise has a glass lens with air on one side and water on the other PLUS a water lens (concave!) with glass on one side and air on the other. In other words, a combination of TWO lenses.

The solution manual deviously inserts a thin layer of air between the lenses so that the n0 can be set to 1 for both lenses.
 
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understand it now finally!
 

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