# Relation Between Lens Length And Imager Size

I was using the calculator to learn the interrelationships between 'subject distance from camera', 'width' and AoV. Keeping everything constant, I changed the imager size from 1/3" to 1" and this changed the focal length. I don't understand how the imager size is related to the focal length.

It would be great if someone could explain this to me.

Thanks.

Take a look at the following image, which shows the cross-section of a lens and how light flows through the lens, hits the convergence point (where the red lines cross), and then goes to the image sensor (the blue line).

If we say the blue line is a 1" image sensor, and the yellow line is a 1/3" image sensor (it's obviously not to scale), you can see how the smaller sensor would be getting less of the overall image from the lens.

Let's assume both imagers produce a 1080p 16:9 output image (imager size has little or nothing to do with final resolution, different sized imagers can produce the same final resolution).

The smaller imager would see only the part of the image that was in the middle part of the larger imager, it is like a zoom effect. Or, to get the same total field of view from the blue imager that the yellow imager sees, you would have to zoom in.

If you hold AOV and scene geometry constant, but change the imager size, you also need to change the lens/focal length to get the same output image.

Holding the lens constant and changing imager size would affect the scene/AOV.

Let me know if that helps/makes sense.

Hi Brian,

Thanks very much for the explanation. It makes complete sense.

Sagar, can you double check if it changed the focal length? From what to what?

Because it should change the AoV but it should not change the focal length. And I just tried switching from 1/3" to 1" and the AoV changed significantly but focal length was the same.

Hi John,

Thanks for your reply. The focal length changed when I forced the AoV to be constant.

I've attached a snapshot of the calculations for your consideration.

In regards to my initial question, I think Brian's reply makes complete sense.

Sure, if you force the AoV to be constant but change the imager size, the focal length needs to change as well.

This is a byproduct that a larger imager produces a wider FoV, all things equal. So when you made the imager much larger (1/3" to 1"), you have to compensate by making the focal length much longer if you want to keep the same AoV.

Hi John,

Thanks for your reply. The focal length changed when I forced the AoV to be constant.

I've attached a snapshot of the calculations for your consideration.

In regards to my initial question, I think Brian's reply makes complete sense.

Great explanation, Brian.

I would only emphasize your statement:

...to get the same total field of view from the [bigger] imager that the [smaller] imager sees, you would have to zoom in.

That part can be counter intuitive. It's also why they put those tiny 1/4" imagers in PTZ's sometimes.

@Sagar, when you say you "forced the AOV to be constant", does that mean that you noted what the AOV was set at with the 1/3" imager, then changed it to 1", and then changed the AOV to what it was before, which in turn changed the focal length?