# Refractive index and focal length

When the refractive index of medium is greater than the lens then what will happen to the focal length of the lens?

## 1 Answer

The sign of the focal length will change. So, a concave lens would behave like a convex lens, and a convex lens as concave lens.

The lens maker’s formula for a thin lens is: $$\dfrac{1}{f} = \left(\dfrac{\mu_2}{\mu_1} -1\right)\left(\dfrac{1}{R _1} - \dfrac{1}{R_2}\right)$$

Where $\mu_2$ is the refractive index of the lens, and $\mu_1$ is the refractive index of the medium.

If $\mu_1 > \mu_2$, then $\frac{\mu_2}{\mu_1} -1 < 0$.

So, the focal length of a convex lens will become negative, and it will act like a concave lens, and focal lens of a concave lens will become positive, so it'll act as a convex lens.