What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

To determine the focal length of a system consisting of a convex lens and a concave lens in contact, we can use the formula for the effective focal length (F) of two thin lenses in contact:

Effective Focal Length Formula

The formula is given by:

1/F = 1/f1 + 1/f2

where:

• F is the effective focal length of the combined lens system.
• f1 is the focal length of the first lens (convex lens).
• f2 is the focal length of the second lens (concave lens).

Identifying the Focal Lengths

In this scenario:

• The convex lens has a focal length of f1 = +30 cm (positive because it converges light).
• The concave lens has a focal length of f2 = -20 cm (negative because it diverges light).

Calculating the Effective Focal Length

Now, we can substitute these values into the formula:

1/F = 1/30 + 1/(-20)

Calculating each term:

• 1/30 = 0.0333
• 1/(-20) = -0.05

Now, adding these values together:

1/F = 0.0333 - 0.05 = -0.0167

Finding the Effective Focal Length

To find F, we take the reciprocal of -0.0167:

F = 1 / -0.0167 ≈ -60 cm

Analyzing the Lens System

The effective focal length of the combined lens system is approximately -60 cm. Since the focal length is negative, this indicates that the system behaves as a diverging lens.

Conclusion on Lens Behavior

In summary, when a convex lens with a focal length of 30 cm is combined with a concave lens of focal length 20 cm, the resulting system has an effective focal length of -60 cm, confirming that it is a diverging lens. This means that the system will spread out light rays that pass through it, rather than converging them to a point.