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Actually, the pictured Fresnel lens in the Hooper Strait lighthouse is a third order lens. I know someone who sat inside it cleaning the glass. Only a very small child could sit inside a fourth order lens.
Maybe, but the NPS has this one listed as a Fourth.
Fourth-Order Fresnel Lens on Display at Hooper Strait Lighthouse
Perhaps after reading this article and studying the photographs, you may agree with me that the NPS has mislabeled that photograph.
Fresnel Lens

And this web page also states that the lens is a third order.

But what do I know?

How many books do you own?