Please explain all work, I need to understand the answer and be able to compare
ID: 1645456 • Letter: P
Question
Please explain all work, I need to understand the answer and be able to compare it to mine more than just know if mine is correct.
The passenger's side-view mirror has writing on it saying "Warning! Objects in the mirror are closer than they appear." The driver's side view mirror does not have this warning. The passenger's side-view mirror is convex with a focal length of -80 cm. A 1.5 m tall cyclist is 25 m from the mirror. You are 1.0 m from the mirror. We will presume, for simplicity, that you, the cyclist and the mirror all lie along a a line.
How far are you from the the image of the cyclist?
How far would you have been in the mirror were flat?
What is the image height?
What would the image height have been in the mirror were flat?
Why is there a label on the passenger's side mirror?
Explanation / Answer
using convex mirror formula we can write
1/F=1/Do+1/Di
where F=- 80cm=.8m , Do=25m Di=?
using formula we get 1/(-.80)=1/25 +1/Di
or-1/.80-1/25=1/Di
or -(1/.80+1/25)=1/Di
or 1/Di=-1.29m
or Di=-1/1.29=-.775m
then my distance from image=-.775-1=-1.775m
In case of plane mirror no such focal length ormula therefore if the object is 25m from the mirror the image is also 25m from the mirror
then I will be 25-1=24m from the image
in case of convex mirror the magnification m=-Di/Do=-(-.775/25)=.031
then the image height=.031* 1.5m=.0465m
in case of flat mirror m=-Di/Do=1
so image height=object height=1.5meter (m*1.5=1*1.5=1.5meter)
The level is the side mirror is due to the features of convex lens. The convex lens o the side view makes the image is smaller and gives a large view of outside while making the issusion of distance. Usually smaller objects appear far from the real distance therefore the caution message is to alert that objects are not that far as it shows.