# Determining the focal length of a compound lens

• Alex_Neof
In summary, the focal length of a compound lens formed by placing a biconvex lens with a focal length of 15 cm in contact with another biconvex lens with a focal length of 25 cm can be found by using the equation 1/f_c = 1/f_1 + 1/f_2. The solution given is +9.375 cm, which uses the absolute values of the focal lengths. However, it was not specified in the course notes whether to use absolute values or not, and not using them would result in a focal length of +37.5 cm. Ultimately, both lenses are biconvex and therefore have positive focal lengths.

## Homework Statement

A biconvex lens, $L_1$, with focal length of magnitude $\left| f_1 \right| = 15$ cm is used with a second biconvex lens, $L_2$, with focal length of magnitude $\left| f_2 \right| = 25$ cm to form a compound lens system.

If the two lenses are placed in mutual contact what is the focal length of the compound lens?

## Homework Equations

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

## The Attempt at a Solution

It's just a matter of plugging into the above equation.. However do I use the the absolute values or the fact that for a biconvex lens

$f_1 > 0$

and

$f_2 < 0$?

Solution given is $+9.375$ cm, which suggests you use the absolute values, however I am not fully convinced as it was not specified in the course notes whether to use absolute values or not.

Not using absolute values, I find the focal length to be $+37.5$ cm

Sorry, I figured it out... both are biconvex lenses therefore their focal lengths are positive. I believe I got confused with radius' of curvatures.. the solution given is the correct one.

For a biconvex lens:

R1 > 0 and R2 < 0 (Radius of curvature)

not the focal lengths...

## 1. What is the focal length of a compound lens?

The focal length of a compound lens is the distance between the lens and the point where parallel rays of light converge after passing through the lens.

## 2. How do you determine the focal length of a compound lens?

The focal length of a compound lens can be determined by placing an object at a known distance from the lens, measuring the distance between the lens and the image formed by the lens, and using the thin lens equation (1/f = 1/u + 1/v) to calculate the focal length.

## 3. Can the focal length of a compound lens be changed?

Yes, the focal length of a compound lens can be changed by adjusting the distance between the lens and the object or the lens and the image, or by changing the shape or refractive index of the lens.

## 4. What factors affect the focal length of a compound lens?

The focal length of a compound lens is affected by the curvature of the lens, the refractive index of the lens material, and the distance between the lens and the object or image.

## 5. Why is it important to determine the focal length of a compound lens?

Determining the focal length of a compound lens is important in understanding how the lens will focus light and create images. It is also crucial in designing and using optical instruments such as cameras, telescopes, and microscopes.