Derive the expression for the focal length of a combination of two thin converging lenses in contact, in terms of their focal lengths.

Derive the expression for the focal length of a combination of two thin converging lenses in contact, in terms of their focal lengths.

or

Show that the effective focal length, f, of two thin lenses in contact is given by                   1/f = 1/ f₁ + 1/f₂ where f₁ and f₂ are the focal lengths of the individual lenses

Solution

Consider two thin lenses L₁ and L₂ of focal length f₁ and f₂.

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