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I have a Canon 18-135 lens. I am looking into the camera viewfinder with my right eye and not through the viewfinder with my left. I start from 18mm and keep zooming in till I see a particular object as the same size with both the eyes.
I read the focal length to be just above 50 mm (say, 55mm). What is special about this 55mm with reference to the object I was focussing on?
There's a specification on (d)SLR bodies called viewfinder magnification; this refers to how large an object appears in the viewfinder when a 50mm lens is mounted and focused at infinity.
On mid-range DSLRs, which typically have around 0.95x magnification, an object will appear to be life-sized at 52.6mm. With entry-level DSLRs, you might have around 0.8x magnification, so you'd have to zoom in to 62.5mm to get a 1:1 magnification. I'm betting your camera has somewhere around 0.9 to 0.95x magnification.
This has very little to do with the object, except that the front of the camera is slightly closer to the object. With far-away subjects (landscapes, etc), the distance between your eyes and the front of your camera won't matter much, but close subjects will appear larger to the camera than to your eye even with a 1:1 magnification.
Little beyond the fact that cameras are designed that way.
They've chosen what they consider a normal lens, and adjust the viewfinder magnification so what you see with a normal lens will approximately match what you see without a viewfinder.
With an APS-C camera, you usually get a magnification of about .9x. With a full (35mm) frame, it's around .75x. A 6x4.5xm medium format usually uses around 0.7x. As you go larger still, the ratio goes down (though larger cameras often have interchangeable viewfinders, often with varying degrees of magnification).
As far as I know, nothing. The viewfinder size depends on the camera so with a different body at the same focal length the object might have a different size.
I've heard the human eye equivalent to roughly a ~45mm lens (on a 35mm camera).
