Answer to Question #206931 in Optics for Faye

Question

A shiny , spherical Christmas tree ornament is 95 mm in diameter
a. Where is the image of a child standing 2.0 m away from the ornament?
b. What is the magnification of the image?
c. Is the image inverted or erect?

Answer 1

Answer:-

(a) We know that relation between focus length and radius of curvature

$f=\frac{R}{2}$

where 2R=D=Diameter

so focal length $f=\frac{D}{4}=\frac{95}{4}\times 10^{-3}meters \\$

and u=-2.0

from convex mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}=\frac{1}{f}-\frac{1}{u}\\ \frac{1}{v}=\frac{1}{(\frac{95}{4}\times 10^{-3})}-\frac{1}{(-2.0)}\\ \boxed{v=0.024m}$

(b) Magnification M=$-\frac{v}{u}\\ =-\frac{0.024}{-2}$

$\boxed{M=+0.012}$

(c) $\because$ Magnification is positive

and image is not inverted then

image is upright.