An object is placed 20 cm in front of a concave spherical mirror that has a radius of curvature 60 cm. Which one of the following phrases best describes the image?

Question

An object is placed 20 cm in front of a concave spherical mirror that has a radius of curvature 60 cm.  Which one of the following phrases best describes the image?

BlackTom AI · Accepted Answer

For spherical mirrors, use the mirror equation 1/f = 1/do + 1/di and the relation f = R/2. Here R = 60 cm for a concave mirror, so f = 60/2 = 30 cm (positive for concave).

Step-by-step calculation:
1. Object distance do = 20 cm (in front of the mirror, taken as positive).
2. Focal length f = +30 cm.
3. Apply the mirror equation:
   1/f = 1/do + 1/di
   1/30 = 1/20 + 1/di
4. Solve for 1/di:
   1/di = 1/30 − 1/20
   Convert to common denominator 60: 1/30 = 2/60, 1/20 = 3/60
   1/di = 2/60 − 3/60 = −1/60
5. Therefore di = −60 cm.

Interpretation: The negative image distance (di = −60 cm) indicates the image is virtual and located on the opposite side of the mirror from where real images form — i.e., behind the mirror — at a distance of 60 cm from the mirror. You can also compute lateral magnification m = −di/do = −(−60)/20 = 3, so the image is upright and three times larger (consistent with a virtual, enlarged image for an object inside the focal length).

Why the correct option is correct:
- di = −60 cm directly matches “virtual and located 60 cm from the mirror.” The negative sign denotes virtual, and the magnitude gives 60 cm.

Why the other options are incorrect:
- “At ∞”: would require the object to be at the focal point (do = f = 30 cm); here do = 20 cm, so not applicable.
- “real and located 60 cm from the mirror”: sign is wrong — di is negative, so the image is virtual, not real.
- “virtual and located 120 cm from the mirror” and “real and located 120 cm from the mirror”: both have the wrong magnitude (calculation gives 60 cm, not 120 cm), and the latter also has the wrong type (real).

Conclusion: The image is virtual and located 60 cm from the mirror, which matches the given answer: "virtual and located 60 cm from the mirror."

An object is placed 20 cm in front of a concave spherical mirror that has a radius of curvature 60 cm. Which one of the following phrases best describes the image?Single choice

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