The Fascinating Optical Phenomenon of Image Formation in a Salad Bowl

Where is the image of your 5.0-cm-tall nose located? What is the image's size?

The image of your 5.0-cm-tall nose is located approximately 17.14 cm from the salad bowl. The image's size is approximately 1.43 cm.

Understanding Image Formation in a Salad Bowl

Image Location: The image of your nose is located inside the bowl, which acts as a concave mirror due to its polished metal surface. The distance from the salad bowl to the image is determined by the mirror equation.

Calculating Image Distance: Using the mirror equation 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Given the radius of curvature of the bowl (48 cm) and the object distance (-60 cm), we find that the image distance is approximately 17.14 cm.

Image Size: The size of the image is determined by the magnification, which is calculated as -di/do. With a magnification of approximately 0.286, the image's height is approximately 1.43 cm.

In conclusion, the image of your 5.0-cm-tall nose is located approximately 17.14 cm from the salad bowl, with an image size of approximately 1.43 cm.