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Waves & Optics Formula

What is Series Combination of Focal Lengths?

Two thin lenses in contact combine by summing their individual powers (reciprocal focal lengths).

Formula: \frac{1}{f_{total}} = \frac{1}{f_1} + \frac{1}{f_2}

Plain-English Meaning

Two thin lenses in contact combine by summing their individual powers (reciprocal focal lengths).

If a waves question feels messy, sketch the geometry or phase relationship first, then return to the algebra.

Deeper Explanation

Two thin lenses in contact combine by summing their individual powers (reciprocal focal lengths).

Worked Example

Problem: Two lenses with f₁ = 20 cm and f₂ = −30 cm are placed in contact. Find f_total.

  • 1/f = 1/20 + 1/(−30) = 3/60 − 2/60 = 1/60
  • f_total = 60 cm

Result: f_total = 60 cm (converging)

At A Glance

Category: Waves & Optics

Levels covered:

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.