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Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is ________.

Asked in GUJCET 2018 · Combinations and silvered lenses

• (1) 1/(f₁f₂)
• (2) (f₁+f₂)/2
• (3) (f₁f₂)/(f₁+f₂)
• (4) (f₁+f₂)/(f₁f₂)

Step-by-step solution

Why the other options are wrong

• (1) comes from multiplies the focal lengths where the powers should be added. 1/(f₁f₂) has the dimensions of m⁻², so it cannot be a power at all.
• (2) comes from averages the two focal lengths. Focal lengths do not average: it is the powers that add, P=1/(f₁)+1/(f₂).
• (3) (f₁f₂)/(f₁+f₂) is the equivalent focal length F of the pair, in metres, not its power. The power asked for is the reciprocal of it.

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