An object is placed 16.7 cm in front of a converging lens with a focal length of 7.4 cm. Calculate the position of the image formed by the lens.Give your answer in cm to 2 decimal places without unitsFor example: 25.00

Question

BlackTom AI · Accepted Answer

Using the thin-lens formula 1/f = 1/do + 1/di, substitute the given focal length and object distance (both positive for a converging lens with a real object).

1. Relevant knowledge points and concepts
- Thin lens equation: 1/f = 1/do + 1/di.
- Sign convention: for a converging lens, f > 0; a real object in front of the lens has do > 0; a positive di indicates a real image on the opposite side of the lens.

2. Complete reasoning process step by step
- Given: f = 7.4 cm, do = 16.7 cm.
- Rearrange for image distance di: 1/di = 1/f − 1/do.

3. Calculations with intermediate steps
- Compute reciprocals:
  1/f = 1/7.4 = 5/37 ≈ 0.1351351351
  1/do = 1/16.7 = 10/167 ≈ 0.0598802395
- Subtract: 1/di = 5/37 − 10/167.
  Use common denominator 37 × 167 = 6179:
  1/di = (835 − 370) / 6179 = 465 / 6179.
- Invert to get di:
  di = 6179 / 465 ≈ 13.2881720430 cm.
- Round to two decimal places (as requested): 13.29

4. Why the correct answer is correct
- The algebraic manipulation of the thin-lens equation and exact fraction arithmetic produce di = 6179/465 ≈ 13.288..., which correctly rounds to 13.29 cm. The positive sign indicates a real image formed on the far side of the lens.

5. Why other possible answers would be incorrect
- A negative value would imply a virtual image (not applicable here because do > f for a converging lens produces a real image).
- Simple arithmetic errors (wrong subtraction of reciprocals or incorrect inversion/rounding) would yield an incorrect di. Any answer significantly different from ~13.29 stems from such mistakes.

6. Conclusion confirming the final answer
- Therefore the image position is 13.29 (two decimal places), matching the provided correct answer.

An object is placed 16.7 cm in front of a converging lens with a focal length of 7.4 cm. Calculate the position of the image formed by the lens.Give your answer in cm to 2 decimal places without unitsFor example: 25.00Numerical

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