How Is the Focal Length of a Mirror Determined When the Image Size Doubles?

[aChordate]

Homework Statement

The image of an object seen in a mirror is twice its actual size. The orientation of the
image is the same as that of the object. If the object distance do is 1.7 m, what is the focal
length of the mirror?

Homework Equations

1/d_o+1/d_i=1/f

m=-d_i/d_o

The Attempt at a Solution

(1/1.7)+1/d_i=1/f


d_i=m*d_o=2*1.7m=3.4

(1/1.7)+(1/3.4)=1/f
f=1.13m

 

[ehild]

Homework Statement

The image of an object seen in a mirror is twice its actual size. The orientation of the
image is the same as that of the object. If the object distance do is 1.7 m, what is the focal
length of the mirror?

Homework Equations

1/d_o+1/d_i=1/f

m=-d_i/d_o

The Attempt at a Solution

(1/1.7)+1/d_i=1/f


d_i=m*d_o=2*1.7m=3.4

(1/1.7)+(1/3.4)=1/f
f=1.13m

di = -mdo = -3.4

ehild

 

[PeterO]

Homework Statement

The image of an object seen in a mirror is twice its actual size. The orientation of the
image is the same as that of the object. If the object distance do is 1.7 m, what is the focal
length of the mirror?

Homework Equations

1/d_o+1/d_i=1/f

m=-d_i/d_o

The Attempt at a Solution

(1/1.7)+1/d_i=1/fd_i=m*d_o=2*1.7m=3.4

(1/1.7)+(1/3.4)=1/f
f=1.13m

For an enlarged image, you must have a concave mirrror. For the image to be upright the object must be inside the focus, so the focal length is going to be bigger that 1.7 m.
A simple sketch of a ray trace will give you this answer in 5 seconds.

If you have drawn enough ray traces before, you will be able to draw this one in your mind rather than committing pencil to paper.
If you haven't drawn enough ray traces to do that, then you better get busy drawing a few more ready for next time.