A convex mirror has a radius of curvature whose magnitude is 41 cm. The mirror i

Question

A convex mirror has a radius of curvature whose magnitude is 41 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 11.0 cm long fluorescent lamp oriented vertically is placed at +95 cm. What is the focal length of the mirror? At what distance from the mirror can we find a sharp image of the lamp? How tall is the image of the lamp? If the convex mirror were replaced by a plane mirror and the lamp moved to 206 cm from the plane mirror, how tall would the image be?

Explanation / Answer

What is the focal length of the mirror?

f = - R/2 = -41/2 = -20.5 cm

At what distance from the mirror can we find a sharp image of the lamp?

1/q = 1/f - 1/p = 1/(-20.5) - 1/95

q = -16.86 cm

How tall is the image of the lamp?

m = h'/h = q/p

h' = qh/p = 16.86 x 11/95 = 1.95 cm

If the convex mirror were replaced by a plane mirror and the lamp moved to 206cm from the plane mirror, how tall would the image be?

11 cm

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