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I understand that a doublet uses different refractive indices:
https://en.wikipedia.org/wiki/Doublet_(lens)
Does an increase in refractive index of either the crown or the flint decrease the focal length of the lens?

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2 Answers 2

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An increase in index of refraction would make a lens bend light more sharply. For the convex lens, it would bring light more sharply toward a focus, and thus decrease the focal length. The concave lens, diverts light away from a short focus toward a longer focus. A higher index of refraction would increase the focal length.

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  • $\begingroup$ Thanks. Is there a specific formula I can refer to for adding extra glass to a plano convex lens? Thats actually what im confused about. How adding extra glass to the plano effects the plano's focal length. Or figuring out how to calculate the change in focal length when the second material's refractive index is changed $\endgroup$ Apr 24, 2020 at 4:48
  • $\begingroup$ It ranges from simple formulae for approximate results to lens design software for complex systems. Start with this. hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenscon.html#c1 $\endgroup$
    – mmesser314
    Apr 24, 2020 at 5:03
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I think your question is too general to answer. The first thing: do you want to increase the refraction index by a certain amount for all wavelengths? If yes (which is impossible in reality.Changing the material, you modify its dispersion in a different way), then it depends on the lens parameters such as surface curvature and numerical aperture. Indeed, these parameters affect the angles between beams and surfaces (air-crown,crown-flint,flint-air).

Consider two opposite cases: blue and red laser beams, focusing by a good achromatic lens approximately in the same focusing point. When you change the refraction index of the material (e.g. crown), you need to do calculations according to the Snell's Law. It states that the multiplication of $n*sin(\theta)$ is conserved, where $\theta$ represents the angle between the beams (incident or refracted) and the mediums interface normal. Changing $n$ of the crown will change the refraction angles $\theta$ approximately in the same way for the red and blue beams, but only for small angles approximation. In this case, the beams bend stronger and the focal length decreases. However, for large angles, bending will occur in different ways for two beams which will lead to focusing of two wavelengths in different places. Practically, your lens is not achromatic anymore.

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  • $\begingroup$ Im actually not sure. Is there a particular calculation/calculator I can refer to for a lens made of two different materials using snells law? I'm curious about changing the refractive index of the second section of the lens. I'd start with a convex lens with a certain focal length, then add a glass blank with the same diameter to this convex lens $\endgroup$ Apr 24, 2020 at 4:58

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