In an experiment to measure the focal length of an equiconvex lens following measurements were made mod [u] = 0.30 mod [v] =0.60 the image formed is real the focal length of lens within error limits is ?

To determine the focal length of an equiconvex lens using the measurements provided, we can apply the lens formula, which relates the object distance (u), image distance (v), and the focal length (f) of the lens. The formula is given by:

Lens Formula

The lens formula is expressed as:

1/f = 1/v - 1/u

Where:

• f = focal length of the lens
• v = image distance (positive for real images)
• u = object distance (negative for real objects)

Given Values

From your measurements:

• Object distance, u = -0.30 m (negative because the object is on the same side as the incoming light)
• Image distance, v = 0.60 m (positive since the image is real)

Calculating the Focal Length

Now, substituting the values into the lens formula:

1/f = 1/v - 1/u

Substituting the values:

1/f = 1/0.60 - 1/(-0.30)

Calculating each term:

1/f = 1/0.60 + 1/0.30

Finding a common denominator (which is 0.60):

1/f = (1 + 2) / 0.60

1/f = 3 / 0.60

1/f = 5

Now, taking the reciprocal to find the focal length:

f = 1/5

f = 0.20 m

Final Result

Thus, the focal length of the equiconvex lens, within error limits, is approximately 0.20 meters or 20 centimeters.

Understanding the Result

This focal length indicates how strongly the lens converges light. A shorter focal length means a stronger lens, while a longer focal length indicates a weaker lens. In practical applications, knowing the focal length helps in designing optical systems, such as cameras and microscopes, where precise control over light is essential.