Since you're at a unit length of 0.5 you can just look at the tangent of the angle which is 0.0875(mm). I'd double check your datasheet to see if that's an approximation based on a larger distance. You may need to add the sensitive area of the die width to that since you are now working in units of microns. If the object was 0.5 meters away, you could neglect the die sensitive area width. When you are very close, the die width will need to be considered.

Interesting question, following to learn

Ron Reiserer thank you. The area I am trying to measure the temperature of is 1.5 mm wide and I am using the Melexis MLX90614xDCI 5° FOV IR sensor to do this (datasheet attached).

I basically need to prove that the sensor, when 0.5mm away from what I am measuring, is measuring the temperature within the 1.5mm width and nothing outside of this width.

The datasheet doesn't detail the dimensions of the aperture on that model. If you look at the package, it looks like they have pressed the TO-39 package in to an aluminum housing. Since that housing is so long, the spot size is going to be big at the opening. You'll need to see if you can measure the aperture down inside that M5 thread.

Based on the published absorber area dimensions and the FOV angle, I'd say the spot size is no larger than 2mm and no smaller than 1mm. This is going to be problematic for the 1.5mm object that you want to measure if it is on the larger side. You may be able to make a smaller aperture and screw it into the M5 thread to narrow the FOV. Since aluminum has a very low emissivity, it would be a good material to use as an aperture. You should make the aperture hole as thin as possible or have a taper greater than the FOV angle with the taper facing in toward the sensor chip.

You may want to change to the K sensor that has 13 degree FOV. Even though the FOV angle is greater, that one has a 0.6mm aperture right at the face of the device. This will make the spot size smaller than 1mm at the distance of 0.5mm.