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Question
Derive the equation for effective focal length for lenses in contact.
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Solution
Lenses in contact
- Two lenses (1) and (2) having focal length are placed coaxially in contact.
- Lens equation for first equation be
`1/"v'" - 1/"u" = 1/"f"_1` - Lens equation for the second lens be
`1/"v" − 1/"v′" = 1/"f"_2` - Adding the above equation
`1/"v" - 1/"u" = 1/"f"_1 + 1/"f"_2` - If the combinations acts as single lens then,
`1/"v" - 1/"u" = 1/"f"` - On comparing,
`1/"F" = 1/"f"_1 + 1/"f"_2`
∴ For any number of lens in contact
`1/"f"_1 + 1/"f"_2 + 1/"f"_3 + ....`
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