Chapter 24. Focal length of a spherical mirror (24-3)

Question

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Question

plsd8F4OGA/OhI1BDmnxkpAOqcaMAbSunBBvyiXwLQ31LomR2ZgSfrbIrZdSCDrMWU124DxqSTA=
{"title":"Focal length of a spherical mirror","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,31,29,97\"}]"} {"title":"Radius of curvature of the mirror","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"93,21,121,56\"}]"}

Review

A glance at Figure 24-11 suggests that the focal length is about half as great as the radius of curvature. In fact, for a concave mirror small enough that all rays parallel to the principal axis are focused at the focal point, the focal length is exactly half of the radius:

Equation 24-3 says that the tighter the curve of a spherical mirror and hence the smaller the radius of curvature r, the shorter the focal length \(f\). (We’ll prove the relationship \(f = r/2\) in Section 24-4.)