Match Perspective and Ortho Cameras

i have a ortho camera looking at a plane positioned and set so that the gameview and the plane are matched (upper-lefft corner of the plane is in the upper-left corner of the screen and the lower-right corner of the plane is at the lower-right corner of the screen)

now i want a perspective camera to show the plane in the same way. i know this can be done by hand but i was wondering:
is there a formula to set a perspective camera-view to match a ortho camera-view at a given distance?

 

You can probably solve it using right triangle math.
The base is the distance from plane, height is the orthographic size of ortho camera.
Then you Can solve the base/hypo angel, which is half your perspective camera fov.
Make syre to match camera rotations. And position camera at plane center, and move it back with your distance.

 

that's simple. thanks.

 

I know this is a very old thread, but in case anyone needs this you can use the following script which is based on @ThermalFusion approach:

Code (CSharp):

1. using UnityEngine;
2.  
3. public class CameraFOV : MonoBehaviour
4. {
5.     [SerializeField]
6.     private float orthographicSize = 5;
7.  
8.     private void Start()
9.     {
10.         Camera camera = GetComponent<Camera>();
11.         float distance = Mathf.Abs(camera.transform.position.z);
12.         camera.fieldOfView = Mathf.Atan2(orthographicSize, distance) * Mathf.Rad2Deg * 2f;
13.     }
14. }
15.  

Note: The code assumes the plane's Z position is 0.