Question

You are given a spherical mirror and wish to determine its properties. You place an object on its axis, 46.5 cm in front of it, and discover that the mirror creates a virtual image located 17.5 cm from the mirror. Determine the mirror's focal length f in centimeters. f= cm Calculate the mirror's radius of curvature C in centimeters. C= cm If it can be determined, is the mirror concave or convex? convex concave cannot be determined

Answer 1

To determine the properties of the spherical mirror, use the mirror formula: 1/f = 1/do + 1/di. The focal length is approximately 27.75 cm, and the radius of curvature is 55.5 cm. The mirror is convex.

Step-by-step explanation:

To determine the properties of the spherical mirror, we can use the mirror formula: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

Given that the object distance is 46.5 cm and the image distance is 17.5 cm, we can substitute these values into the formula:

1/f = 1/46.5 + 1/17.5

Simplifying this expression, we find that the focal length of the mirror is approximately 27.75 cm.

The radius of curvature, C, is equal to twice the focal length, so C = 2 * 27.75 = 55.5 cm.

Since the focal length of the mirror is positive, we can determine that the mirror is convex.

Answer 2

The focal length (f) of the mirror is -28.9 cm, indicating that the mirror is convex. The radius of curvature (C) is -57.8 cm.

Step-by-step explanation:

To determine the focal length and radius of curvature of a spherical mirror, we can use the mirror formula:

1/f = 1/do + 1/di

Where f is the focal length, do is the object distance, and di is the image distance.

Given that the object distance (do) is 46.5 cm and the image distance (di) is 17.5 cm, we can substitute these values into the formula and solve for f:

1/f = 1/46.5 + 1/17.5

Calculating this expression gives us f = -28.9 cm

The negative sign indicates that the mirror is convex.

Since the focal length is the reciprocal of the sum of the object and image distances, we can calculate the radius of curvature (C) as 2f:

C = 2f = 2(-28.9) = -57.8 cm