To solve this problem, we need to analyze the behavior of light and images formed by a concave mirror. The u-v method involves understanding the relationship between the object distance (u), the image distance (v), and the focal length (f) of the mirror. Let's break down the situation step by step.
Understanding the Setup
In this experiment, the object pin A is placed on the principal axis of a concave mirror at a distance x from the mirror's pole P. The student observes the inverted image of this pin. The key point here is the observation that when the student shifts their eye to the left, the image appears to move to the right of the object pin.
Analyzing the Image Formation
For a concave mirror, the image characteristics depend on the position of the object relative to the focal point (f) and the center of curvature (C), which is located at a distance of 2f from the mirror. The behavior of the image can be summarized as follows:
- If the object is placed between the focal point (f) and the mirror (x < f), the image formed is virtual, upright, and located on the same side as the object.
- If the object is at the focal point (x = f), the rays of light are parallel after reflection, and no image is formed at a finite distance.
- If the object is placed beyond the focal point but before the center of curvature (f < x < 2f), the image is real, inverted, and located on the opposite side of the mirror.
- If the object is at the center of curvature (x = 2f), the image is real, inverted, and of the same size as the object.
- If the object is placed beyond the center of curvature (x > 2f), the image is real, inverted, and smaller than the object.
Interpreting the Observation
Now, let's focus on the observation made by the student. When the student shifts their eye to the left and sees the image moving to the right, it indicates that the image is on the opposite side of the mirror and is real. This behavior is characteristic of an object placed beyond the focal point.
Determining the Correct Range for x
Given that the image appears to the right of the object pin when the eye is shifted, we can conclude that the object pin A must be positioned such that:
- The object distance x is greater than the focal length f (x > f).
- However, since the image is real and inverted, it must also be beyond the focal point but not necessarily beyond the center of curvature. Therefore, we can conclude that x must be greater than f but less than or equal to 2f.
Final Conclusion
Based on this analysis, the correct answer to the question is (B) f < x < 2f. This indicates that the object pin A is positioned between the focal point and the center of curvature of the concave mirror, resulting in a real, inverted image that behaves as described in the observation.
