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

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:

$\boxed{20 \text{ cm}}.$