Question

In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance (x) and the image distance (y) are measured with reference to the focal point of the lens. The y-x plot is shown in figure.
The focal length of the lens is_____cm.

Answer 1

Correct Answer: 20

From the lens formula:

\[\frac{1}{f} = \frac{1}{x} + \frac{1}{y}.\]

The plot shows the relationship between y (image distance) and x (object distance). For any specific point on the graph, the values of x and y can be substituted into the lens formula to calculate f.

Alternatively, the product of x and y at corresponding points can be used to directly calculate the focal length. From the lens equation, we know:

\[x \cdot y = f^2.\]

From the graph: - At point C, x = 20 cm and y = 20 cm.

Using \(x \cdot y = f^2\):

\[f^2 = 20 \cdot 20 = 400.\]

Taking the square root:

\[f = \sqrt{400} = 20 \text{ cm}.\]

Final Answer: The focal length of the lens is:

\[\boxed{20 \text{ cm}}.\]