Question

A person 1.8m tall stands 0.75m from a reflecting globe in a garden.

Answer 1

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 = $\frac{r}{2}$ = $\frac{0.08}{2}$ = 0.04 m

1. The image distance, v, can be determined by applying mirror formula:

$\frac{1}{f}$ = $\frac{1}{u}$ + $\frac{1}{v}$

$\frac{1}{0.04}$ = $\frac{1}{0.75}$ + $\frac{1}{v}$

$\frac{4}{100}$ - $\frac{75}{100}$ = $\frac{1}{v}$

$\frac{1}{v}$ = $\frac{4 - 75}{100}$

  = - $\frac{71}{100}$

⇒ v = -$\frac{100}{71}$

      = - 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.  $\frac{image distance}{object distance}$ = $\frac{image height}{object height}$

  $\frac{1.41}{0.75}$ = $\frac{v}{1.8}$

v = $\frac{2.538}{0.75}$

  = 3.384

v = 3.38 m

The person's image is 3.38 m tall.