An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. (b) Determine the position, size, orientation, and nature (real or virtual) of the

Verified step by step guidance

1. Step 1: Calculate the focal length (f) of the concave mirror using the radius of curvature (R). The formula to find the focal length is f = R / 2.
2. Step 2: Use the mirror equation to find the image distance (di). The mirror equation is 1/f = 1/do + 1/di, where do is the object distance from the mirror.
3. Step 3: Determine the magnification (m) of the image using the magnification formula m = -di / do. This will help in finding the image size and its orientation.
4. Step 4: Calculate the image size using the magnification. The height of the image (hi) can be found by multiplying the object height (ho) by the magnification, hi = ho * m.
5. Step 5: Analyze the sign of the image distance (di) and the magnification (m) to determine the nature (real or virtual) and orientation (upright or inverted) of the image. If di is positive, the image is real and inverted; if di is negative, the image is virtual and upright.

Key Concepts

Concave Mirror

A concave mirror is a spherical mirror that curves inward, resembling a portion of a sphere. It can converge light rays that are parallel to its principal axis, allowing for the formation of real or virtual images depending on the object's position relative to the focal point. The focal length of a concave mirror is half its radius of curvature, which is crucial for image formation calculations.

Mirror Formula

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror, expressed as 1/f = 1/v + 1/u. This equation is essential for determining the position of the image formed by the mirror. The sign conventions for distances must be carefully applied, where distances measured in the direction of the incoming light are negative.

Magnification

Magnification is the ratio of the height of the image (h') to the height of the object (h), given by the formula magnification (m) = h'/h = -v/u. It indicates how much larger or smaller the image is compared to the object and also provides information about the orientation of the image. A positive magnification indicates an upright image, while a negative value indicates an inverted image.