Question

At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror's radius of curvature is 0.574 m. (a) Locate the image of a patient 10.6 m from the mirror. (Use the correct sign conventions.)
cm (from the mirror)

(b) Indicate whether the image is upright or inverted.

upright inverted    

(c) Determine the magnification of the image.

Answer 1

Solution:-

Given –

Radius of curvature – 0.574 m

A convex mirror always produces an image that is, diminished behind mirror upright virtual.

a)      Focal length f = 0.287 m (1/2 radius of curvature and virtual)

Object distance, u = 10.6 m

V – Image distance

1/u + 1/v = -1/0.287 m

1/v = -1/0.287 – 1/10.6

1/v = 3.3899

V = 0.294 m

Or v = 29.4 cm (behind mirror, virtual)

c)      Calculate magnification

M = -v/u

M = - (-0.294 / 10.6)

M = 0.027 (upright image)

b)     Answer of b part is mentioned in a and c