The real image of a concave mirror is six times as large as the object.

(a) Determine the image distance for an object that is 39.4 cm from the mirror. (Include the appropriate positive or negative sign.)

(b) Determine the focal length of the mirror.

Question

High School

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Answer :

Steve511 Steve511 · Answer 1 · 2024-03-25T23:38:12-04:00

To find the image distance, we use the magnification equation. To find the focal length, we use the mirror equation.

To determine the image distance for an object that is 39.4 cm from the mirror, first, we can use the magnification equation:

magnification (m) = -image distance (di) / object distance (do)

Given that the magnification is 6, we can rearrange the equation to solve for the image distance:

di / do = -6

Substituting the values, we have:

di / 39.4 cm = -6

Simplifying the equation, we find that the image distance (di) is -236.4 cm.

To determine the focal length of the mirror, we can use the mirror equation:

1/focal length (f) = 1/image distance (di) + 1/object distance (do)

Substituting the values and solving for the focal length, we have:

1/f = 1/-236.4 cm + 1/39.4 cm

Simplifying the equation, we find that the focal length (f) is -39.4 cm.

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