A goldfish lives in a -diameter spherical fish bowl. The fish sees a cat watching it. If the cat's face is from the edge of the bowl, how far from the edge does the fish see it as being? (You can ignore the thin glass wall of the bowl.)
The cat seems to be away from the edge of the bowl.
The refraction image from surface by
When the light strikes a media with an index of refraction of and is refracted by a medium with an index of refraction of . If the surface is convex toward the item, the radius of curvature is positive; otherwise, it is negative.
Consider the paraxial rays that refract from the air into the water using the cat as a point source. The rays originating from the air bubble are refracted toward the normal at the surface because where is the index of refraction of air, and the cat's face seems farther from the edge of the bowl than it actually is.
The convex towards cat is
A keratometer is an optical device used to measure the radius of curvature of the eye’s cornea—its entrance surface. This measurement is especially important when fitting contact lenses, which must match the cornea’s curvature. Most light incident on the eye is transmitted into the eye, but some light reflects from the cornea, which, due to its curvature, acts like a convex mirror. The keratometer places a small, illuminated ring of known diameter 7.5 cm in front of the eye. The optometrist, using an eyepiece, looks through the center of this ring and sees a small virtual image of the ring that appears to be behind the cornea. The optometrist uses a scale inside the eyepiece to measure the diameter of the image and calculate its magnification. Suppose the optometrist finds that the magnification for one patient is 0.049. What is the absolute value of the radius of curvature of her cornea?
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