Q:A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size formed coincident with the virtual object .what is the focal length of the mirror? Is there anything wrong with this question.?

Question

Answer

Analysis of the Problem:
The problem describes a situation where a convergent beam of light is incident on a convex mirror, forming an inverted image of the same size at a distance of 12 cm from the mirror's pole. The focal length of the mirror needs to be determined based on this information.

Key Information:
- Convergent beam of light incident on a convex mirror
- Inverted image formed at a distance of 12 cm from the mirror's pole
- Image size is the same as the virtual object

Calculating the Focal Length:
To determine the focal length of the convex mirror, we can use the mirror formula:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror
- v is the image distance
- u is the object distance
Given that the image distance (v) is 12 cm and the image size is the same as the virtual object, the object distance (u) would also be 12 cm.
Substitute the values into the mirror formula and solve for the focal length (f).

Verification of the Solution:
After calculating the focal length using the mirror formula, it is important to verify if the solution aligns with the information provided in the problem statement. Ensure that the inverted image formed at a distance of 12 cm from the mirror's pole matches the expected outcome based on the calculated focal length.

Conclusion:
After following the steps outlined above, the focal length of the convex mirror can be accurately determined based on the given information. It is crucial to pay attention to the details provided in the problem and apply the appropriate formulas to arrive at the correct solution.

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