To find the power of a combination of two thin convex lenses, we use the formula for the equivalent focal length $ f_{\text{eq}} $ of the lens system when the lenses are placed coaxially with a certain distance $ d $ between them:

$ \frac{1}{f_{\text{eq}}} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2} $

Given:

$ f_1 = 30 \, \text{cm} $

$ f_2 = 10 \, \text{cm} $

$ d = 10 \, \text{cm} $ (distance between the two lenses)

First, convert the focal lengths from centimeters to meters:

$ f_1 = 0.3 \, \text{m} $

$ f_2 = 0.1 \, \text{m} $

Plug in the values into the equation:

$ \frac{1}{f_{\text{eq}}} = \frac{1}{0.3} + \frac{1}{0.1} - \frac{0.1}{(0.3)(0.1)} $

Calculate each term:

$ \frac{1}{0.3} = \frac{10}{3} \approx 3.33 $

$ \frac{1}{0.1} = 10 $

$ \frac{0.1}{(0.3)(0.1)} = \frac{0.1}{0.03} = \frac{10}{3} \approx 3.33 $

Substitute these calculated values back into the formula:

$ \frac{1}{f_{\text{eq}}} = 3.33 + 10 - 3.33 $

$ \frac{1}{f_{\text{eq}}} = 10 $

Thus, the power of the lens combination is:

$ \text{Power} = \frac{1}{f_{\text{eq}}} = 10 \, \text{D} $

Therefore, the power of the lens system is 10 diopters (D).