An object is located so that a virtual image is formed -8 cm behind a concave mirror that has a 7.9 cm focal length. Calculate the object distance.

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BlackTom AI · Accepted Answer

Question restatement: An object is positioned so that a virtual image is formed 8 cm behind a concave mirror with a focal length of 7.9 cm. Find the object distance.

Step-by-step approach: To analyze mirrors, we use the mirror (thin lens) equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. For concave mirrors, the focal length is positive. A virtual image is formed behind the mirror, which, under the standard sign convention, means di is negative (since it lies on the same side as the object, behind the mirror).

Plug in the known values: f = +7.9 cm, di = -8 cm. Then 1/do = 1/f − 1/di = 1/7.9 − 1/(-8) = 1/7.9 + 1/8.

Compute the numerical values: 1/7.9 ≈ 0.12658 and 1/8 = 0.125. Adding them gives 0.25158. Therefore do ≈ 1 / 0.25158 ≈ 3.97 cm.

Rounding considerations: Depending on significant figures or rounding conventions, you might report the object distance as roughly 3.97 cm, which is about 4.0 cm when rounded to two significant figures. If someone arrives at 4.2 cm, that would imply a slightly different intermediate rounding or a variation in sign convention for di; the standard derivation with di = -8 cm leads to ≈3.97 cm.

Conceptual notes: The key ideas are using the mirror equation, applying the sign convention correctly (concave mirror has positive f; virtual image behind the mirror gives di negative), and solving for do. Misapplying signs or mixing up the virtual/real designation can yield notably different results, such as a much larger object distance or an incorrect sign for do.

Summary without final verdict: Following the standard sign convention and the mirror equation with di = -8 cm and f = +7.9 cm yields an object distance do on the order of 4.0 cm, demonstrating how the interplay between focal length and image location constrains where the object must be placed relative to the mirror.

An object is located so that a virtual image is formed -8 cm behind a concave mirror that has a 7.9 cm focal length. Calculate the object distance.

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