A convex mirror has a radius of curvature whose magnitude is 55 cm. The mirror i

Question

A convex mirror has a radius of curvature whose magnitude is 55 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 5.5 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 230 cm from the plane mirror, how tall would the image be?

Explanation / Answer

Focal length, f = R/2 = 55/2 = 27.5 cm

Given , u = 95 cm

we have

1/f = 1/u+1/v

1/v = 1/f-1/u

1/v = 1/27.5 - 1/95

v = 38.7 cm

Image is formed at 38.7 cm from mirror.

m = hf/hi = v/u

hf = 5.5 * 38.7/95 = 2.24 cm

Height of image = 2.24 cm

Focal length of a plane mirror is f = .

so, v = u = 230 cm

Height = same = 5.5 cm

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