The focal length of the second biconvex lens is $ f_2 $.

The focal length of the third biconcave lens, due to Cartesian sign conventions, is $-f_3$.

Power of Combined Lenses

Combination of the First and Second Biconvex Lenses:

The reciprocal of the combined focal length is given by:

$ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} $

Therefore, the power of the combination of the first and second lenses, $ P_1 $, is:

$ P_1 = \frac{1}{f} = \frac{f_1 + f_2}{f_1 f_2} $

Combination of the First Biconvex and Third Biconcave Lens:

The reciprocal of the combined focal length is:

$ \frac{1}{f} = \frac{1}{f_1} - \frac{1}{f_3} $

Thus, the power of this combination, $ P_2 $, is:

$ P_2 = \frac{1}{f} = \frac{f_3 - f_1}{f_1 f_3} $

Combination of the Second Biconvex and Third Biconcave Lens:

The reciprocal of the combined focal length is:

$ \frac{1}{f} = \frac{1}{f_2} - \frac{1}{f_3} $

Therefore, the power of the second and third lens combination, $ P_3 $, is:

$ P_3 = \frac{1}{f} = \frac{f_3 - f_2}{f_2 f_3} $

These calculations show how we derive the combined power of lenses using their individual focal lengths and considering the sign convention for convex and concave lenses.

Ray Optics

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