Question

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

PART A If the diameter of the globe is 16cm , where is the image of the person, relative to the surface of the globe?
PART B How large is the person's image?

Answer 1

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.

Step-by-step 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 =
`(r)/(2)` =
`(0.08)/(2)` = 0.04 m

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

`(1)/(f)` =
`(1)/(u)` +
`(1)/(v)`

`(1)/(0.04)` =
`(1)/(0.75)` +
`(1)/(v)`

`(4)/(100)` -
`(75)/(100)` =
`(1)/(v)`

`(1)/(v)` =
`(4 - 75)/(100)`

= -
`(71)/(100)`

⇒ v = -
`(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.
`(image distance)/(object distance)` =
`(image height)/(object height)`

`(1.41)/(0.75)` =
`(v)/(1.8)`

v =
`(2.538)/(0.75)`

= 3.384

v = 3.38 m

The person's image is 3.38 m tall.