# How does focal length change in an achromat with a change of refractive index?

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?

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.