Could someone please check my math on required focal length?

[Michael Holmes]

This is a basic question, but I just want to be sure I'm not making a mistake.
I have been using a 1/3" sensor camera.
Now I will be using two FS100 cameras for two-camera shoots, and I am checking the lenses I need.
With the Super 35mm sensor size, the needed focal length seems huge.

My math is the basic math for similar triangles:
L/W = focal length/sensor width

So, if I want a close-up of say 4 ft width, and I want to shoot it from the back of a club, say 35 ft away from the musician, I would get:
focal length = 35 x 23.6mm/4 = 206mm

If I want a 3 ft. wide close-up, the focal length would need to be:
focal length = 35 x 23.6/3 = 275mm

This is low light shooting and I plan to go with a Nikon 70-200 f/2.8 lens for the close-up camera. But if my math is right, the zoom will be near max most of the time. I don't want to get real close to the musicians, so I stay out of the way of the other camera shots.

I am sure I am making a math mistake.........what is it?

[Eric Olson]

Originally Posted by Michael Holmes

I am sure I am making a math mistake.........what is it?

Given the crop factor of 1.5 the Nikon lens on the Sony FS100 ranges from a 35mm equivalent of 100 to 300mm. The Canon XF100 which you were using before ranges from a 35mm equivalent of 30 to 300mm. Thus both cameras have about the same reach. How much did you need to zoom the XF100?

[Michael Holmes]

I didn't have it fully extended, but I usually had it most of the way.

Help me with the math. Since the FS100 sensor is almost three times as wide as the 1/3" XF100 sensor, I was assuming the required focal length increased by a factor of three. This of course would lead to a very long reach. What is wrong with this logic?

I just want to understand how you are figuring it.
How do you arrive at the crop factor?
Is that the equivalent of going through the math I went through?

Thanks!

[Doug Jensen]

You might find this field of view calculator helpful.
AbelCine - Field of View Calculator

[Eric Olson]

Originally Posted by Michael Holmes

Since the FS100 sensor is almost three times as wide as the 1/3" XF100 sensor, I was assuming the required focal length increased by a factor of three.

More precisely the sensor in the FS100 is 4.7 times wider than the XF100. Remember 1/3" refers to the diameter of the vacuum tube that would have housed the sensor at some mythical time in the past.

Crop factor is figured by comparing with a full 36x24mm frame. It is useful because photographers are already familiar with how subjects frame using a 35mm camera. The calculation for the FS100 is

36/23.6=1.52 crop factor

The crop factor for the XF100 is 36/5=7.2x and the actual lens has focal lengths from 4.25 to 42.5mm. Thus the 35mm equivalent focal lengths are 30 to 300mm.

The XF300 has the same sensor size and crop factor but a 4.1 to 73.8mm lens. Thus the 35mm equivalent focal lengths are 29 to 530mm.

[Michael Holmes]

Originally Posted by Eric Olson

More precisely the sensor in the FS100 is 4.7 times wider than the XF100. Remember 1/3" refers to the diameter of the vacuum tube that would have housed the sensor at some mythical time in the past.

Crop factor is figured by comparing with a full 36x24mm frame. It is useful because photographers are already familiar with how subjects frame using a 35mm camera. The calculation for the FS100 is

36/23.6=1.52 crop factor

The crop factor for the XF100 is 36/5=7.2x the actual lens has focal lengths from 4.25 to 42.5mm. Thus the 35mm equivalent focal lengths are 30 to 300mm.

The XF300 has the same sensor size and crop factor but a 4.1 to 73.8mm lens. Thus the 35mm equivalent focal lengths are 29 to 530mm.

Perfect, Eric.
Now I understand what you are doing. :)
Thank you.