Question

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A convex mirror has a radius of curvature whose magnitude is 51 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 7.0 cm long fluorescent lamp oriented vertically is placed at +108 cm. 1.)What is the focal length of the mirror?

2.)At what distance from the mirror can we find a sharp image of the lamp? Tries 0/5 How tall is the image of the lamp?

3.)If the convex mirror were replaced by a plane mirror and the lamp moved to 190 cm from the plane mirror, how tall would the image be?

Answer 1

for convex mirror focal length is negative

focal length is -R/2 = -51/2 = -25.5 cm

object height is ho = 7 cm

image height is hi = ?

focal length is f = -25.5 cm

object distance is do = 108 cm

then using

1/f = 1/do + 1/di

1/di = 1/f - 1/do = (-1/25.5) - (1/108)

di = -20.62 cm

So at a distance of20.62 cm we can find a sharp image of the lamp

magnification m = -di/do = hi/ho

height of the image is hi = -ho*(di/do) = (7*20.62)/108 = 1.33 cm

3) in case of plane mirror

image distance di = object distance do = 190 cm

tehn height of the image is hi = ho*(di/do) = 7*(190/190) = 7 cm