Question

Please answer as soon as possible!

A 3.0 cm object is 12.0 cm from a convex mirror that has a focal length of 20.0 cm.
What is the distance of the image from the mirror?
____cm
What is the height of the image?
___cm

Answer 1

-30 and 7.5

Step-by-step explanation:

Answer 2

(a) The mirror equation which relates the focal length f, the distance of the object
`d_o` and the distance of the image
`d_i` is

`(1)/(f)= (1)/(d_o) + (1)/(d_i)`
where for sign convention we take the focal length of a convex mirror as negative :
`f=-20 cm`.
Since we know the distance of the object from the mirror,
`d_o=12 cm`, we can find the distance of the image:

`(1)/(-20)= (1)/(12) + (1)/(d_i)`
from which

`d_i=-7.52 cm`
where the negative sign means the image is virtual (located behind the mirror).

(b) We can find the height of the image through the magnification (M) equation:
`M= (h_i)/(h_o)= -(d_i)/(d_o)`
where
`h_i` and
`h_o` are the height of the image and the object, respectively
.Using
`h_o=3 cm` we can find
`h_i`:

`h_i=h_o ( (-d_i)/(d_o))=(3 cm)( (7.52 cm)/(12 cm) )=1.88 cm`
where the positive sign means the image is upright.