Question

a concave spherical mirror has a radius of curvature of 27.6 cm . the object distance is 45.5 cm. Find the location of the image for the following object distances. For each case, state whether the image is real or virtual and upright or inverted and find the magnification. (In each case, use the correct sign conventions for all answers. If the image is located at infinity, enter the word infinity for the image distance and for the magnification.) (a) object distance = 40.0 cm image distance: Answer in cm. magnification:

Answer 1

By using the mirror equation and the magnification formula, we can determine the image location and magnification for a specific object distance. For an object distance of 40.0 cm in a concave mirror with a radius of curvature of 27.6 cm, the image distance we get is approximately -32.4 cm. Thus, we have a real image that is inverted and smaller than the object (magnification of 0.81).

Step-by-step explanation:

To determine the image location and magnification for various object distances in a concave mirror, we can use the mirror equation 1/f=1/di +1/do, where f represents the focal length of the mirror, di is the image distance, and do is the object distance. Given that the radius of curvature (R) of the mirror is 27.6 cm, the focal length (f) will be half of the radius of curvature, which equals 13.8 cm.

For the object distance of 40.0 cm, we can rewrite the mirror equation as 1/di = 1/f - 1/do. Fill in the given values to get 1/di = 1/13.8 - 1/40.0, which gives us di, the image distance, as approximately -32.4 cm. The negative sign indicates that the image is formed on the same side as the light source, making it a real image. Since it's a real image, it's also inverted.

To find the magnification (m), we can use the equation m = -di/do. Filling in the values, we get m = -(-32.4 cm)/40.0 cm = 0.81. The positive magnification indicates the image is upright, while its value less than 1 represents the image is smaller than the object itself.

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