A convex mirror has a radius of curvature whose magnitude is 41 cm. The mirror i
ID: 1380240 • Letter: A
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 11.5 cm long fluorescent lamp oriented vertically is placed at +101 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
given that ::
radius of curvature of convex mirror, R = - 41 cm
object distance, d0 = 101 cm
focal length of the mirror is given as :
f = R / 2 { eq. 1 }
inserting the value of R in eq.1,
f = - (41 cm) / 2 = - 20.5 cm
using converging formula,
1 / di + 1 / d0 = 1 / f { eq. 2 }
a sharp image of the lamp is given as :
1 / di = 1 / f - 1 / d0
inserting the values in above eq.
1 / di = 1 / (- 20.5 cm) + 1 / (101 cm) = - 121.5 / 2070.5
di = - 17.04 cm
using magnification formula,
How tall is the image of the lamp is given as :
m = - ( di / d0 ) { eq. 3 }
inserting values in eq. 3,
m = - ( - 17.04 cm / 101 cm ) = 0.168
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 given as ::
In this case, the image remains the same, which is to be 11.5 cm.