# Can focal length of convex lens be negative?

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A convex lens in a medium with index larger than that of the lens will act like a divergent lens, yes. This is the physical fact. If you consider the focal length positive or negative will depend on the convention used. By usual convention, the focal lens of divergent lenses is taken with minus sign. If you use the lens-maker formula (in the thin lens approximation) $$\frac{1}{f}=(n_{lens} -n_{medium})(\frac{1}{R_1}- \frac{1}{R_2})$$ you can see that if $\ n_{lens} <n_{medium}$ the focal length will be negative. Note that the formula is written with the convention that $R_2$ is negative for convex lenses so that the content of the second parenthesis on the RHS is always positive for convex lenses.

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### Nalin Raj

Updated on May 26, 2020

• Nalin Raj almost 3 years

Is focal length of convex lens negative when it is surrounded by a medium with greater refractive index than that of lens?

• engineer over 6 years
I would argue that you're talking about a concave lens of the other medium with a positive focal length then.
• Nalin Raj over 6 years
No there no necessity for a convex to have r2 greater than r1
• Priyanka over 6 years
I didn't say that. You didn't mention the type of convex lens. If you consider it ti be biconvex in a denser medium then it can not have negative focal length irrespective of the relation between R1 and R2. I think you didn't undersrand what I said. Read it properly once again.
• M. Enns over 6 years
There is going to be some reflection whenever light goes into another medium with a different refractive index (larger or smaller) but why do you say it would act as a concave mirror rather then convex?