The correct option is **B. At the principal focus**. ### Detailed Explanation: To understand why placing an object at the principal focus of a concave mirror results in an image at infinity, we need to delve into the properties of concave mirrors and the formation of images. 1. **Understanding Concave Mirrors**: - A concave mirror is a spherical mirror that curves inward, resembling a portion of the interior of a sphere. - Key points associated with concave mirrors include: - **Pole (P)**: The midpoint of the mirror's surface. - **Principal Focus (F)**: The point where parallel rays of light either converge (for real images) or appear to diverge from (for virtual images) after reflecting off the mirror. For concave mirrors, this point is located in front of the mirror. - **Center of Curvature (C)**: The center of the sphere from which the mirror is a part. It is located behind the mirror. 2. **Image Formation**: - The behavior of light rays when they strike a concave mirror is governed by the mirror formula and ray diagrams. - The mirror formula is given by: \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \] where: - \( f \) is the focal length (distance from the mirror to the focus), - \( d_o \) is the object distance (distance from the mirror to the object), - \( d_i \) is the image distance (distance from the mirror to the image). 3. **Positioning the Object**: - When an object is placed at the **principal focus (F)** of a concave mirror, the light rays emanating from the object travel towards the mirror parallel to the principal axis. Upon reflection, these rays diverge as if they are coming from a point at infinity. - Mathematically, when \( d_o = f \) (the object is at the focus), the mirror formula simplifies to: \[ \frac{1}{f} = \frac{1}{f} + \frac{1}{d_i} \] This implies that \( d_i \) approaches infinity, indicating that the image is formed at infinity. ### Why Other Options Are Incorrect: - **A. At the pole of the mirror**: - If the object is placed at the pole, the rays will reflect and diverge, forming a virtual image behind the mirror. The image will not be at infinity; instead, it will be located at a distance less than the focal length. - **C. At the center of the curvature**: - When the object is placed at the center of curvature (C), the rays will reflect back through the center, forming a real image at the same distance as the object (i.e., at the center of curvature). This does not produce an image at infinity. - **D. Between the principal focus and the center of curvature**: - If the object is placed between the principal focus and the center of curvature, the rays will converge to form a real image beyond the center of curvature. This image will not be at infinity but at a finite distance. ### Summary: - The correct position for an object to create an image at infinity in front of a concave mirror is at the **principal focus**. - Light rays from the object at the focus reflect parallel to the principal axis, leading to an image at infinity. - Other positions (pole, center of curvature, between focus and center) do not yield an image at infinity. ### Revision Summary: - **Concave mirrors focus parallel rays at the principal focus.** - **Placing an object at the principal focus results in an image at infinity.** - **Other positions yield finite images, not at infinity.** - **Use the mirror formula to analyze object and image distances.**