Angle of View Maths Question

[meanwhile]

Hi All,

Have a maths question that I thought I could work out, and gave it a go, but get stuck half-way.

A7 II - 36 x 24 sensor - 6000 x 4000 pixels.

Theoretical 35mm lens - take a photo.

Wondering, how do I work out mathematically how many pixels I should crop it to to have the same angle of view in the image as a theoretical 40mm lens?

It's a bit of a silly question, but now I'm stuck on the maths of it.

 

[Hye]

Hi All,

Have a maths question that I thought I could work out, and gave it a go, but get stuck half-way.

A7 II - 36 x 24 sensor - 6000 x 4000 pixels.

Theoretical 35mm lens - take a photo.

Wondering, how do I work out mathematically how many pixels I should crop it to to have the same angle of view in the image as a theoretical 40mm lens?

It's a bit of a silly question, but now I'm stuck on the maths of it.

This boils down to similar triangles.

Draw a triangle with a sensor height of 4000 pixels, and set the focal point 40mm away.

Now if you actually had a 35mm lens, then the sensor would actually be a bit closer to the focal point. If you wanted the same angle of view as the 40mm lens, then you want to find the pixel height corresponding to where the 40mm triangle intersects the sensor that is 35mm away.

By similar triangles, the height/4000 = 35mm/40mm, or 3500 pixels.

Repeat for the width.

If you need a diagram, let me know, and I'll figure out how to upload one.

HTH

 

[meanwhile]

This boils down to similar triangles.

Draw a triangle with a sensor height of 4000 pixels, and set the focal point 40mm away.

...snip...

By similar triangles, the height/4000 = 35mm/40mm, or 3500 pixels.

Repeat for the width.

If you need a diagram, let me know, and I'll figure out how to upload one.

With trial and error I worked out it's around 5400 x 3600, but it could just be that my 35mm and 40mm aren't actually 35mm and 40mm exactly.

I'll try it with triangles, as you suggest.

Now if you actually had a 35mm lens, then the sensor would actually be a bit closer to the focal point. If you wanted the same angle of view as the 40mm lens, then you want to find the pixel height corresponding to where the 40mm triangle intersects the sensor that is 35mm away.

Thank you for that simple mental picture, that clarifies a lot. It may seem obvious (and may BE obvious), but your explanation ticked a box in my head that for some reason wasn't ticked.

 

[Pixel Pooper]

You just multiply by the ratio of the focal lengths, 35/40 = 0.875 so you would need (6000 x 0.875) x ( 4000 x 0.875) which is 5250 x 3500.

If you want to use megapixels instead you multiply by the ratio twice so 24 x 0.875 x 0.875 = 18.37MP.