Comment by dredmorbius

The way you're phrasing this may be misleading.

The strength of a password / passphrase increases with the power of 2 raised to the bits of entropy.

That's an exponential proportion, rather than a linear one. But a proportion all the same.

Example:

Given mixed-case alphanumeric (62 characters) and an 8-character password length, the number of combinations is:

    62^8 = 218,340,105,584,896 (keyspace -- 218 quadrillion)
    l(62^8)/l(2) = 47.6 (bits of entropy)

A 10 character password (if randomly chosen from the same character set) has 10^17 possibly combinations (about 4,000x more), and 59.4 bits of entropy, 11.8 bits more. 2^11 = 2048.