Suppose I model the forward swap rate lognormal

$$dS\_t = \sigma\_{ln}S\_tdW\_t$$

On the other hand we could model it simply by a normal assumption:

$$dS\_t = \sigma\_{n}dW\_t$$

I would like to know if there is a relationship for the volatilities $\sigma\_n,\sigma\_{ln}$? A friend told me, that he saw the approximation

$$\sigma\_n\approx \sigma\_{ln}S\_t$$

However, neither my friend nor I was able to come up with a justification of this approximation. So is this a valid approximation? If so, why and if not, how else can I relate the two volatilities?