Answer:
1. The image of the person is 1.41 m, virtual and formed at the back of the surface of the globe.
2. The person's image is 3.38 m tall.
Explanation:
From the given question, object distance, u = 0.75 m, object height = 1.8 m, radius of curvature of the reflecting globe, r = 8 cm = 0.08 m.
f = [tex]\frac{r}{2}[/tex] = [tex]\frac{0.08}{2}[/tex] = 0.04 m
1. The image distance, v, can be determined by applying mirror formula:
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{u}[/tex] + [tex]\frac{1}{v}[/tex]
[tex]\frac{1}{0.04}[/tex] = [tex]\frac{1}{0.75}[/tex] + [tex]\frac{1}{v}[/tex]
[tex]\frac{4}{100}[/tex] - [tex]\frac{75}{100}[/tex] = [tex]\frac{1}{v}[/tex]
[tex]\frac{1}{v}[/tex] = [tex]\frac{4 - 75}{100}[/tex]
= - [tex]\frac{71}{100}[/tex]
⇒ v = -[tex]\frac{100}{71}[/tex]
= - 1.41 m
The image of the person is 1.41 m, virtual and formed at the back of the surface of the globe.
2. [tex]\frac{image distance}{object distance}[/tex] = [tex]\frac{image height}{object height}[/tex]
[tex]\frac{1.41}{0.75}[/tex] = [tex]\frac{v}{1.8}[/tex]
v = [tex]\frac{2.538}{0.75}[/tex]
= 3.384
v = 3.38 m
The person's image is 3.38 m tall.
