You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. (a) Where is the of your 5.0-cm-tall nose located?

Verified step by step guidance

1. Identify the type of mirror used in the problem. Since the bowl is spherical and polished, it acts as a concave mirror.
2. Determine the focal length of the mirror using the mirror equation for a spherical mirror: \( f = \frac{R}{2} \), where \( R \) is the radius of curvature.
3. Use the mirror equation \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \) to find the image distance \( d_i \). Here, \( d_o \) is the object distance (distance from the mirror to your nose) and \( f \) is the focal length.
4. Determine the nature of the image (real or virtual, upright or inverted) by analyzing the sign of \( d_i \) and using the mirror formula. If \( d_i \) is positive, the image is real and inverted; if negative, the image is virtual and upright.
5. Calculate the magnification of the image using the magnification formula \( m = -\frac{d_i}{d_o} \), where \( m \) is the magnification factor. Use this to find the height of the image by multiplying \( m \) with the object height (height of your nose).

Key Concepts

Spherical Mirrors

Spherical mirrors are reflective surfaces shaped like a portion of a sphere. They can be concave or convex, affecting how they reflect light. In this scenario, the salad bowl acts as a concave mirror, which can focus light and form images of objects placed in front of it, such as the nose.

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. For a concave mirror, the focal length is positive, and this formula helps determine where the image of an object will form based on its distance from the mirror.

Image Formation

Image formation in mirrors involves the interaction of light rays with the reflective surface. For concave mirrors, depending on the object's position relative to the focal point, images can be real or virtual, upright or inverted, and magnified or reduced. Understanding this concept is crucial for locating the image of the nose in relation to the bowl.