Chapter 24. Lensmaker’s equation for the focal length of a thin lens (24-24)

Question

1gbOxJyjY4qI7V4WF2+YcgPWAsaK42fjlXpIZvwH5HnEBRtJZbdal3Scg8A=

{"title":"Focal length of a lens surrounded by air","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"4,40,20,75\"}]"} {"title":"Index of refraction of the lens material","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"70,26,89,48\"}]"} {"title":"Radius of curvature of lens surface 2 (the surface farther from the object)","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"249,39,271,68\"}]"} {"title":"Radius of curvature of lens surface 1 (the surface closer to the object)","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"172,40,194,69\"}]"}

Question

RRzyzq7irEN47hOs84E3E/aG6S6lc0TXQpuhlNcVb++Sd/bJC/bHL7pE0d4=

{"title":"Focal length of a lens surrounded by air","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\":\"4,40,20,75\"}]"} {"title":"Index of refraction of the lens material","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"70,26,89,48\"}]"} {"title":"Radius of curvature of lens surface 2 (the surface farther from the object)","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"249,39,271,68\"}]"} {"title":"Radius of curvature of lens surface 1 (the surface closer to the object)","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"172,40,194,69\"}]"}

Question

e9n0G5tPjGRR42QyZLfuw5tDD+qVAEhjEqzesDTVfPvKMNLqzDEP4zaA7fPb9JK8HThyTy1Wx2837xd0g+4KWRJxYO1Jczqn5gVk0s+hbJg=

{"title":"Focal length of a lens surrounded by air","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\":\"4,40,20,75\"}]"} {"title":"Index of refraction of the lens material","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"70,26,89,48\"}]"} {"title":"Radius of curvature of lens surface 2 (the surface farther from the object)","description":"Correct!","type":"correct","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"249,39,271,68\"}]"} {"title":"Radius of curvature of lens surface 1 (the surface closer to the object)","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"172,40,194,69\"}]"}

Question

MVhRFHH9pebU5IJLwghCfBKSr0V1RboWW/pUtlM3O/rk7t3d4TnOBAxyZ56kD2hrHIPZcdTqJcZcqxPHCT5LtBSSSs97ugVwAxYB/g==

{"title":"Focal length of a lens surrounded by air","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\":\"4,40,20,75\"}]"} {"title":"Index of refraction of the lens material","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"70,26,89,48\"}]"} {"title":"Radius of curvature of lens surface 2 (the surface farther from the object)","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"249,39,271,68\"}]"} {"title":"Radius of curvature of lens surface 1 (the surface closer to the object)","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"172,40,194,69\"}]"}

Review

Equation 24-24 can be derived by applying Snell’s law of refraction (Equation 23-6) to a ray of light refracted by both surfaces of a lens. The derivation is beyond our scope, however.

The values of the radii of curvature \(R_1\) and \(R_2\) depend on how sharply and in what direction the two surfaces of the lens are curved. As Figure 24-34 shows, we take a radius to be positive if the center of curvature is on the other side of the lens from the object, but negative if the center of curvature is on the same side as the object. For example, in Figure 24-34 the radius \(R_1\) of surface 1 is positive, but the radius \(R_1\) of surface 2 is negative.