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

To determine the focal length of the equiconvex lens, we use the lens formula:

1/f = 1/v - 1/u

where:

f = focal length of the lens
u = object distance (0.30 m)
v = image distance (0.60 m)
Step 1: Substitute the values into the lens formula
1/f = 1/0.60 - 1/0.30

Step 2: Calculate the reciprocals
1/0.60 = 1.6667
1/0.30 = 3.3333

Step 3: Compute the difference
1/f = 1.6667 - 3.3333
1/f = -1.6667

Step 4: Compute f
f = -1 / (-1.6667)
f = 0.60 m

Step 5: Determine error limits
For error estimation, assume typical measurement uncertainties in u and v to be ±0.01 m. We propagate errors using the formula:

df/f = (du/u) + (dv/v)

df/0.60 = (0.01/0.30) + (0.01/0.60)
df/0.60 = 0.0333 + 0.0167
df = 0.03 m

Final Answer:
The focal length of the equiconvex lens within error limits is 0.60 ± 0.03 m.