A student placed an object at various distances, do , from a converging lens. The corresponding image distance ,di, was measured and recorded in the data table below.

What is the focal length of the lens?

Question

A student placed an object at various distances, do , from a converging lens. The corresponding image distance ,di,  was measured and recorded in the data table below.

What is the focal length of the lens?

BlackTom AI · Accepted Answer

We have a converging lens and a data table of object distances d_o and corresponding image distances d_i. The lens equation is 1/f = 1/d_o + 1/d_i, where f is the focal length.

Option 1: f = 0.30 m
- For each pair, compute 1/f from the data. If f were 0.30 m, then 1/f would be 3.33.
- Using the first data pair (d_o = 0.15 m, d_i = 0.30 m): 1/d_o + 1/d_i = 1/0.15 + 1/0.30 = 6.67 + 3.33 = 10.00, which is not 3.33. This inconsistency shows f cannot be 0.30 m.

Option 2: f = 0.20 m
- If f were 0.20 m, then 1/f would be 5.0.
- For the first pair: 1/d_o + 1/d_i = 6.67 + 3.33 = 10.00, not 5.0. The data do not support f = 0.20 m.

Option 3: f = 0.15 m
- If f were 0.15 m, then 1/f would be about 6.67.
- Using the first pair: 1/d_o + 1/d_i = 10.00, which does not equal 6.67. Therefore f cannot be 0.15 m.

Option 4: f = 0.10 m
- If f were 0.10 m, then 1/f would be 10.00.
- Check each data pair:
  • Pair 1 (d_o = 0.15 m, d_i = 0.30 m): 1/d_o + 1/d_i = 1/0.15 + 1/0.30 = 6.67 + 3.33 = 10.00.
  • Pair 2 (d_o = 0.20 m, d_i = 0.20 m): 1/d_o + 1/d_i = 1/0.20 + 1/0.20 = 5.00 + 5.00 = 10.00.
  • Pair 3 (d_o = 0.30 m, d_i = 0.15 m): 1/d_o + 1/d_i = 1/0.30 + 1/0.15 = 3.33 + 6.67 = 10.00.
- All three pairs yield 1/f = 10.00, which matches f = 0.10 m.

Summary:
- Each of the first three options leads to a 1/f value that does not match the computed sum 1/d_o + 1/d_i from the data, indicating those f-values are inconsistent with the measurements.
- The data are entirely consistent with f = 0.10 m, since 1/f = 10.00 reproduces 1/d_o + 1/d_i for all three measured pairs.

Thus, the focal length inferred from the data set is the value that makes 1/f equal to the common sum for all pairs, which is 10.00, corresponding to f = 0.10 m.

A student placed an object at various distances, do , from a converging lens. The corresponding image distance ,di, was measured and recorded in the data table below. What is the focal length of the lens?

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