Question #c8fa6
1 Answer
See below.
Explanation:
The focal length of a mirror
If the object is placed 9 cm in front of the mirror and 4 cm from the focal point (I assume), that indicates that the focal point is located in front of the mirror, making this a concave mirror. The focal length is then 5 cm.
The mirror equation (also used for thin lenses) is given by:
#1/f=1/d_"o"+1/d_i#
where
We are given:
-
#d_o=9"cm"# -
#f=5"cm"# -
#h_o=4"cm"#
We can begin by finding
#=>1/d_i=1/f-1/d_o#
#=>d_i=(1/f-1/d_o)^-1#
Using our known values:
#d_i=(1/5-1/9)^-1#
#=(9/45-5/45)^-1#
#=(4/45)^-1#
#=45/4#
So
Since the mirror is located at 9 cm from the object, this indicates the the image is formed behind the object and in front of the mirror. This means that the image is real.
Now that we know
#m=h_i/h_o=-d_i/d_o#
#m=-d_i/d_o#
#=-(45/4)/9#
#=-45/36#
Then we have:
#h_i=h_o*m#
#=4*-45/36#
#=-180/36#
#=-5#
So
This means that the image is inverted.