What Should Be the Radius of Curvature of the Other Surface?

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SUMMARY

The discussion centers on calculating the radius of curvature for a corrective lens with a prescription of +1.50 diopters, using the lensmaker's equation. The lens material has a refractive index (n) of 1.46 and a preformed convex front surface with a radius of curvature (R1) of 19.0 cm. The correct approach involves converting the diopter value to focal length in meters and ensuring consistent units throughout the calculations. The initial attempt at solving the equation was incorrect due to unit discrepancies.

PREREQUISITES
  • Understanding of lensmaker's equation
  • Knowledge of diopters and focal length conversion
  • Familiarity with refractive indices
  • Ability to perform unit conversions (cm to meters)
NEXT STEPS
  • Review the lensmaker's equation and its applications in optics
  • Learn about the relationship between diopters and focal length
  • Practice unit conversion techniques, especially in optics
  • Explore common errors in lens calculations and how to avoid them
USEFUL FOR

Students studying optics, optical engineers, and anyone involved in lens design or corrective eyewear manufacturing.

lostfan176
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Homework Statement



A prescription for a corrective lens calls for +1.50 diopters. The lensmaker grinds the lens from a "blank" with n = 1.46 and a preformed convex front surface of radius of curvature of 19.0 cm. What should be the radius of curvature of the other surface?


Homework Equations



<br /> \frac{1}{f} = (n-1)\left ( \frac{1}{R_1} - \frac{1}{ R_2} \right ) <br />

The Attempt at a Solution



1.5=(1.46 - 1)(1/19 - 1/x)

(1.5/.46) - 1/19 = 3.208
-1/3.208 = -.3117

which is wrong
am i doing this right cause i don't think i am
 
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Hi lostfan176,

One thing I see: the value in diopters of a lens is the inverse of the focal length in meters. When you wrote 1/f=1.5, you chose your units of length in meters, but then you wrote R1 in centimeters.
 

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