Question

You combine two thin lenses by placing them in contact so that their axes coincide, forming what is called a compound lens. The focal lengths of the lenses are 20.3 cm and –51.3 cm, respectively. Find the focal length of this compound lens.

Answer 1

The focal length of the compound lens formed by placing two thin lenses in contact is approximately 33.7 cm.

Step-by-step explanation:

In order to find the focal length of the compound lens formed by placing two thin lenses in contact, we can use the formula for the combined focal length of two lenses:

1/f = 1/f₁ + 1/f₂

where f is the combined focal length, f₁ is the focal length of the first lens, and f₂ is the focal length of the second lens.

Substituting the given values, we have:

1/f = 1/20.3 - 1/51.3

Simplifying this equation gives us the reciprocal of the combined focal length:

1/f = (51.3 - 20.3)/(20.3 * 51.3) = 31/1044.99

Taking the reciprocal of this value, we find:

f = 1044.99/31

Therefore, the focal length of the compound lens is approximately 33.7 cm.