Optics: Glass Bead & Center of Curvature

[tangur]

Let's say we have an objet O in front on a glass bead. The first surface will be a convex surface, hence the centre of curvature is in the back of the surface, which gives $$+R_1$$. The object, is a real object in front of the surface, which makes it $$+p_1$$, however for the second refraction, we take $$q_1$$ which becomes $$-p_2$$ + the diameter of the glass bead.Hopefully I have grasped everything right so far, now what I'm not quite so sure about, does surface 2 have its centre of curvature in the back or in the front of the surface. Logically, I'm thinking the center of curvature is inside since the surface 2 is ). Which will give $$-R_2$$.

What I want to be sure to understand, if we have a ) refractice surface, the center of curvature is in front of the surface, and with a ( refracting surface, the center of curvature is in the back of the surface. If i picture the center of curvature as the point were you'd stick the compass in order to make a circle, is that correct?

Thanks in advance

 

[Valerie Park]

!Yes, that is correct. For a convex surface (curve outwards) the center of curvature is in the back of the surface and for a concave surface (curve inwards) the center of curvature is in the front of the surface. If you picture the center of curvature as the point where you would stick the compass to draw a circle then you got it right.

 

[Graeme Robinson]

Your understanding of the optics principles is correct. The center of curvature for a convex surface is located behind the surface, while for a concave surface it is located in front of the surface. This can be visualized as the point where a compass would be placed to draw a circle, as you mentioned.

In the case of a glass bead, the second surface would also be convex, so the center of curvature would be behind the surface again. However, the diameter of the glass bead would need to be taken into account when calculating the distance between the two surfaces, as you correctly mentioned.

Keep in mind that the center of curvature is a theoretical point and may not always be physically present in an actual object. It is used in calculations to determine the refraction of light at the surface.

Overall, your understanding of optics and the placement of the center of curvature is correct. Keep up the good work!