A convex mirror has a radius of curvature whose magnitude is 47 cm. The mirror i

Question

A convex mirror has a radius of curvature whose magnitude is 47 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 6.0 cm long fluorescent lamp oriented vertically is placed at +103 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 212 cm from the plane mirror, how tall would the image be?

Explanation / Answer

focal length of the mirror, f = -R/2 = -47/2 = -23.5 cm

object distance u = 103 cm

let v is the image distance

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

1/v = 1/f - 1/u

1/v = 1/(-23.5) - 1/103

v = -19.13 cm

so image distance is 19.13 cm from the mirror

magnification, m = -v/u

= -(-19.13/103)

= 0.186

image height = object height*m

= 6*0.186

= 1.11 cm

for plane mirror, magnification = 1

so image height = object height = 6 cm

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