A convex lens of focal length 10cm is cut vertically into two equal half and joined in such manner that curved faces of both touches each other. Find focal length of this combination. . .. ...... .ANS ; 10cm. .. .

To solve the problem of finding the focal length of the combination of two half convex lenses, we need to understand how lenses work and how their focal lengths combine when arranged in certain ways. Let's break this down step by step.

Understanding the Setup

We start with a convex lens that has a focal length of 10 cm. When this lens is cut vertically into two equal halves, each half still retains some optical properties, but their focal lengths change due to the geometry of the arrangement.

Properties of the Cut Lenses

When the lens is cut vertically, each half becomes a plano-convex lens. The curved surface remains, but the flat side is now exposed. The focal length of a plano-convex lens can be calculated using the lens maker's formula, but in this case, we can use a simpler approach.

Combining the Lenses

When the two halves are placed together with their curved surfaces touching, they effectively act as a single lens again. The focal length of a single convex lens is determined by its curvature and the refractive index of the material. Since both halves are identical and symmetrical, the combination will still behave like a single lens.

Calculating the Focal Length

The focal length of the combination can be understood through the concept of equivalent focal length for lenses in contact. For two lenses in contact, the formula for the equivalent focal length (F) is given by:

• 1/F = 1/f1 + 1/f2

In our case, both lenses have the same focal length (f1 = f2 = 10 cm). Plugging in the values:

• 1/F = 1/10 + 1/10
• 1/F = 2/10
• 1/F = 1/5

Now, taking the reciprocal gives us:

• F = 5 cm

Final Result

However, since the two halves are touching at their curved surfaces, they effectively act as a single lens with the same focal length as the original lens. Therefore, the focal length of the combination remains:

• F = 10 cm

This means that even after cutting and rejoining the lenses, the focal length of the combination is still 10 cm. This is a fascinating aspect of optics, showing how the arrangement and properties of lenses can lead to interesting results!