Zee Ley, long time no contact, great to hear from you. You have a legitimate question. Spherical shapes are something that I like myself. I have several 40mm spheres in various types of quartz and one 150mm clear quartz sphere, yes it is a crystal ball. The crystal ball sits right beside me when I at the computer. It weighs a little more than 10 pounds, quite impressive. But back to your ball, this is the hard way (easy way later). First you need to identify the properties of the spherical object. It may be just glass, it might be something else (from leaded glass, quartz, …). Different materials can have an effect on the focus point, causing distortion.
A warning note to all. The spherical clear object be it glass or quartz or whatever, can be used as a magnifying glass, and very well I might say. And the larger the sphere the greater the ability to focus light into a pinpoint inferno. I found this out as I got my crystal ball years ago during one Christmas. It sat on a counter until springtime when the sunlight began to hit it. There was an orchid nearby. Needless to say, there are two perfect holes burned thru overlapping leaves that were in the focus point. We quickly moved the crystal ball to a corner where sunlight and moonlight will not hit it. Yes, moonlight can produce an effect at this size also. Just be careful of where you sit this sphere shape.
Now your sphere, calculate the volume of the item. Quartz has a density of 0.0957 lb/in³. Glass is 0.0867 lb/in³ in density. They are close in density. I get this data from
http://www.matweb.com. The next step is to weigh your sphere. You should be able to see close results. I say this because glass when properly poured will produce a calculatable answer to these formula’s.
http://www.physicsinsights.org/simple_optics_spherical_lenses-1.html This site is everything you ever wanted to know about calculating this item. This is a two part calculation. There is a formula for going to a spherical shape to a flat. And another set to calculate from the flat to the spherical focal point. You have to calculate the entrance of the sphere, shown lower on page, and use this data to drive the upper half. Now Quartz can distort this anywhere up to 10%. Quartz crystal, grown through tectonic processes, can distort light. The larger the sphere, the larger possible deviation. And it can be quite different as you spin the sphere.
Now the easy way, please do not start a fire doing this. You just take it out in the sunlight. Take some kind of material where you could see burning but be able to easily put it out. You do not need to get it burning, smoke will do. A piece of harder firewood chunk will do easily. If you are worried about starting something on fire, have some water close by to douse it, just in case. You can see the focal point on sunlight as you change the distance of the sphere to the substance. It is approximately 1/3 to 2/3 of the sphere diameter.
Now the bigger problem is you cannot focus on anything but one point. Any object larger than the head of a pin will be distorted, and you will probably even get some distortion there. Of note: I can see about a half of fingertip clearly on my 150mm crystal ball. Well that is our math and science lesion for the day. Have a great day and thanks for bringing this up Zee Ley, Haiku …