Question

How can be calculated total focal length and power when two lenses are in contact.

Answer 1

Answer on Question #65380, Physics / Optics

How can be calculated total focal length and power when two lenses are in contact.

Solution:

Focal length $F$ of two thin lenses in contact is given by:

$$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \quad (1),$$

where $f_1$ and $f_2$ are the focal lengths of two thin lenses.

Of (1) $\Rightarrow F = \frac{f_1 \times f_2}{f_1 + f_2}$ (2)

Power $P$ of two thin lenses in contact is given by:

$$P = P_1 + P_2 \quad (3),$$

where $P_1$ and $P_2$ are the powers of two thin lenses.

Relationship between power $P$ and focal length $F$:

$$P = \frac{1}{F} \quad (4)$$

(2) in (4):

$$P = \frac{f_1 + f_2}{f_1 \times f_2}$$

Answer:

Total focal length: $F = \frac{f_1 \times f_2}{f_1 + f_2}$

Total power: $P = \frac{f_1 + f_2}{f_1 \times f_2}$

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