A useful quantitative model for the grinding of lenses with known focal lengths is the lens-makers'...

 

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A useful quantitative model for the grinding of lenses with known focal lengths is the lens-makers' equation: nlens environment 1) (1/4-1/2), where f is the focal length of the lens, the two index of refraction are for the material of the lens and the environment it will be used in (typically air, environment 1.00), and R and R the radii of curvature for the front (side facing the incoming light) and back of the lens respectively. a. You need to grind a lens, lens = 1.55, to improve the vision of a child. They need a lens with an optical power of -.800 diopters, if one side of the lens is flat, what must the radius of curvature of the other side of the lens be? Should it be a concave or convex surface? Explain your thinking. b. This child has a near point at 10.0 cm from the lens of their eye and a far point (with eyes relaxed) at 125 cm. Assuming the retina is 2.00 cm behind the lens of their eye, over what range (in diopters) does the power of this child's eyes vary? c. Explain how the lens you made in part a will assist this child with their vision. A useful quantitative model for the grinding of lenses with known focal lengths is the lens-makers' equation: nlens environment 1) (1/4-1/2), where f is the focal length of the lens, the two index of refraction are for the material of the lens and the environment it will be used in (typically air, environment 1.00), and R and R the radii of curvature for the front (side facing the incoming light) and back of the lens respectively. a. You need to grind a lens, lens = 1.55, to improve the vision of a child. They need a lens with an optical power of -.800 diopters, if one side of the lens is flat, what must the radius of curvature of the other side of the lens be? Should it be a concave or convex surface? Explain your thinking. b. This child has a near point at 10.0 cm from the lens of their eye and a far point (with eyes relaxed) at 125 cm. Assuming the retina is 2.00 cm behind the lens of their eye, over what range (in diopters) does the power of this child's eyes vary? c. Explain how the lens you made in part a will assist this child with their vision.