The diagram below shows an object located at point P, 0.25 meter from a concave spherical mirror with principal focus F. The focal length of the mirror is 0.10 meter.

How does the image change as the object is moved from point P toward point F?

Question

The diagram below shows an object located at point P, 0.25 meter from a concave spherical mirror with principal focus F. The focal length of the mirror is 0.10 meter.

How does the image change as the object is moved from point P toward point F?

BlackTom AI · Accepted Answer

The scenario involves a concave mirror with focal length f = 0.10 m. The object starts at do = 0.25 m from the mirror and is moved toward the focal point F (do decreases from 0.25 m toward 0.10 m).

Option A: It’s distance from the mirror increases and the size of the image decreases.
- As the object moves toward the focal point, the image distance di actually increases (approaching infinity as do → f). Therefore, the first part is incorrect. 
- Additionally, the magnification |m| = di/do grows as di increases while do decreases, so the image size does not shrink; it tends to grow larger, especially as do gets close to f. Thus this option is not accurate.

Option B: It’s distance from the mirror decreases and the size of the image increases.
- The distance of the image from the mirror di increases while the object approaches F, not decreases. The second part about increasing size is partly true, but the first part is wrong, making this option incorrect.

Option C: It’s distance from the mirror increases and the size of the image increases.
- This aligns with the physics: as do decreases toward f, the image distance di increases toward infinity, so the image moves farther from the mirror. At the same time, the magnification |m| = di/do grows, so the image becomes larger in size. The combined trend is that the image moves away from the mirror and grows in size.

Option D: It’s distance from the mirror decreases and the size of the image decreases.
- Both aspects are opposite to what happens: di does not decrease as the object moves toward F; it increases. Additionally, the image size does not uniformly shrink under these conditions. Hence this option is incorrect.

In summary, evaluating each statement against the relationships given by 1/f = 1/do + 1/di and m = -di/do shows that the behavior described in Option C best matches the expected optical behavior as the object moves from P toward F.

The diagram below shows an object located at point P, 0.25 meter from a concave spherical mirror with principal focus F. The focal length of the mirror is 0.10 meter. How does the image change as the object is moved from point P toward point F?

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