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The optical interval between two thin lenses having focal lengths f₁ and f₂ and separated by a distance d is ________.

Asked in GUJCET 2016 · Combinations and silvered lenses

• (1) d+(f₁+f₂)
• (2) d-(f₁+f₂)
• (3) d+(f₁-f₂)
• (4) d-(f₁-f₂)

Step-by-step solution

Why the other options are wrong

• (1) comes from adds the focal lengths to the separation instead of taking them out of it. The interval is what is left of d after both focal distances have been used up, so it is always shorter than d.
• (3) comes from uses the difference of the focal lengths and then adds it on. Each lens eats its own focal length out of the gap, so the two focal lengths are added together and then subtracted.
• (4) d-(f₁-f₂) returns d for two identical lenses, but two lenses of focal length f a distance d apart have an optical interval d-2f.

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