Equivalent focal length of lens underwater

Hi everyone,

I have a Nikon D70 with the 18-70mm kit lens. I use the kit lens at 18mm focal length (my rig does not allow change of focal length) behind a FLAT port. Taking into account the 1.5 times focal length multiplication for Nikon cameras and the fact that my port is flat, what is the equivalent focal length of my set-up?

Is it same as my old Nikonos with its 35mm lens?

Thanks in advance for any reply.

Have you actually used this rig underwater. If not, I would be very surprised if you find the image quality acceptable at 18mm behind a flat port. You really should be using a dome port for wide angle lenses.

Behind a flat port there will be some pretty noticable distortion/softness.

I agree William,

Mistakenly I once installed this lens on a D70 behind an Ike flat port - it suffered extreme 'tunnel vision'. It might work at the 70mm end but not at the 18.

I could even find a picture somewhere - it was quite horrid.

Paul C

Hi,

I have used it underwater, the quality is not good but acceptable. I thought it is wider than a 35mm lens on my Nikonos but the vendor of the rig say it is equivalent.

Below is an example taken in Sipadan recently.

Hi,

 

I have used it underwater, the quality is not good but acceptable. I thought it is wider than a 35mm lens on my Nikonos but the vendor of the rig say it is equivalent.

 

Below is an example taken in Sipadan recently.

I'm new here...sorry. What is the best focal length lens to use underwater on a NikonD300 rig? Fixed or zoom...any opinions?

In vacuum (and approximately in air) the field of view has angular width in radians

      theta[air]=2 arctan(L/2 f)

where f is the focal length and L is the width of the sensor, and theta is in radians.  But, usually field of view is quoted for the diagonal, and in that case L=sqrt(w^2+h^2), where w is width and h is height.

If the lens is directed through a flat port into water, then the field of view has angular width given by Snell's Law:

      theta[water] = 2 arcsin( sin( theta[air] /2)/1.333 )

where 1.333 is the index of refraction of water.

For example:

The D70 sensor is 23.7 by 15.6 mm, so it measures 28.37mm diagonally. Then, an 18mm lens has field of view in air of

theta[D70,air] =2 arctan(28.37/2*18) = 1.335 radians

Convert radians to degrees by multiplying by (180/pi) = 57.29:

theta[D70,air] = 1.335 * 57.29 = 76 degrees ::  is the field of view of a D70 with 18mm lens in air.

A full-frame sensor is 36x24 mm, so 43.27mm diagonally. Then, a 27mm lens would have field of view

theta[FF,air] =1.34 radians = 77 degrees  ::  is the field of view of a FF sensor with 18mm lens in air.

This is almost the same as the 18mm lens for the D70. The ratio. (27 mm/18 mm) is the "Nikon factor" of 1.5, to account for the smaller sensor.

In water, the D70 with a flat port would have field of view

theta[D70,water] = 2 arcsin( sin( 1.335 /2) /1.333) = 0.965 radians = 55 deg  ::  FOV of a D70 w/ 18mm lens in water.

With a little algebra, you can show that this is the same field of view as a 41mm lens with a full-frame sensor in air, or with your D70 in air with a 27mm lens.

I hope this helps! 

The rule of thumb is that a flat port magnifies the image by about 1.25x.  So your 18mm lens becomes an 18mm x 1.5x crop factor = 27mm lens.  Then accounting for the fact it's behind a flat port it becomes 27 x 1.25 = 33.8 mm lens, so for all intents and purposes roughly equivalent to a 35mm lens in air.

However the 35mm Nikonos had a reduced field of view underwater compared to a 35mm lens in air - it was roughly equivalent to a 47 mm lens in air.   So your 18mm lens will have a wider field than a 35mm nikonos.   If you set your 18-70 to about 25mm it will be equivalent field of view to the 35mm Nikonos.  This is because it's a 35mm focal length lens behind a flat port.

That said , the quality behind a flat port at 18mm will not be great, corners will be a little mushy and will have chromatic abberation.

The issue is not magnification or focus multiplication because whilst the camera will appear to magnify the working distance in water is also increasing so the net effect is zero because you have a longer lens further away resulting in the same shot.

The problem are pincushion distortion and the amount of water between you and the subject making it not worth to take anything behind a flat port that is not 35mm equivalent or longer

This was well explained in an article from David Knight from the now defunct cameras underwater and similar material can be read on scubageek

So your 18mm lens with crop is 27mm and this will give some undesired effect albeit not as bad as if you had a 10mm lens