A convex spherical mirror has a radius of curvature of magnitude 46.0 cm. (a) De

Question

A convex spherical mirror has a radius of curvature of magnitude 46.0 cm. (a) Determine the position of the virtual image and the magnification for object distances of 41.0 cm. Indicate the location of the image with the sign of your answer. image location = cm magnification = (b) Determine the position of the virtual image and the magnification for object distances of 57.0 cm. Indicate the location of the image with the sign of your answer. image location = cm magnification = (c) Are the images in parts (a) and (b) upright or inverted? The image in part (a) is The image n part (b) is

Explanation / Answer

focal length, f1 = R/2 = -46/2 = -23 cm

a)

let u and v are object and image distances.

u = 41 cm

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/(-23) - 1/41

v = -14.73 cm

magnification, m = -v/u

= -(14.73/41)

= -0.359

b) Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/(-23) - 1/57

v = -16.38 cm

magnification, m = -v/u

= -(16.38/57)

= -0.2875

C) The image in part a) is inverted

The image in part b) is inverted

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