Calculating Focal Length Range for Projector with Varying Distances

[questions_uk]

Hi. There's a question that has given some variables which am not sure how to compute to some previous lens/optics equations. These are not the actual variable values by the way.

If a projector (square pixel SXGA) has a diagonal size of 5 mm which uses a screen of 1 m in which the distances vary from 1 to 2 m, how would the focal length range be calculated?

Would you just calculate the focal length at 2 m, then 1 m then take these values away giving the range?

And would the 1/f = 1 / u + 1 / v equation be used? It is the diagonal size and horizontal size that am not sure about.

Thanks.

 

[mgb_phys]

Just draw a diagram
The ray goes from one corner of the screen pixel through the lens centre to one corner of the focal plane pixel.
The distance from the centre of the lens to the focal plane is the focal length
Then it's just similair triangles if you know all the other dimensions.

 

[questions_uk]

Thank you for your reply. Is the distance not from the lens to the screen? And would it not be 1/f = 1 / u + 1 / v? Am also not sure where triangles would come into calculating the focal length.

Thanks.