Can a 1.7m person see their full reflection in a 0.85m mirror on the wall?

[jimbo43]

A flat mirror that is 0.85m tall is attached to a wall so that its upper edge is 1.7m above the floor. Use the law of reflection and a ray diagram to determine if this mirror will show a person who is 1.7m tall his or her complete reflection.

Please help me as I do not know what to do. So tell me if this is correct...

Height = 0.85m
P = 1.7m
Q = ?

What does the person's height 1.7m above go into? Please help me as I am seriously confused about this problem and have been stuck on it for hours.

 

[mgb_phys]

Draw a line from the top of the person to the bottom of the mirror.
Work out what angle this bounces of the mirror.
Where on the person does the reflected ray reach?

 

[jimbo43]

Can you further clarify this? How would I find the angle that this bounces off the mirror. And where will it reflected ray reach on the person.

 

[mgb_phys]

I think the question is asking can the person see their feet in the mirror?
So you are interested in where the lowest possible ray reflected off the mirror goes.
The law for the angle a ray reflects from a plkane mirror is rather simple.
You know the path from the person to the mirror (you probably have to assume their eyes are at the top of their head!)

You would normally need the distance from the person to the wall but there is something special about 1.7m and 0.85m !

 

[jimbo43]

So is the answer that if the person stands far enough from the mirror he might be able to see his entire self?

 

[mgb_phys]

Yes (if the mirror was placed half way up )
But draw the diagram for the heights given in the question and what do you find, no matter how close you draw the person to the mirror?

 

[jimbo43]

The person will see more top half of himself?

 

[mgb_phys]

Draw a person, now draw a wall some distance away.
Draw a ray from the top of the person to a point on the wall at half their height.
Now draw the ray reflecting from the wall and going back to them - you know about mirrors, what angle will the ray bounce off the mirror?
Now try and draw a ray that hits the wall a little bit higher than the middle - where will that reflect? What can you say about rays that hit the wall above half way?

Notice that the mirror in the questions extends down to halfway up the person.

 

[jimbo43]

Thanks for helping me on this. You helped me greatly.