How Is Object Distance Calculated in Mirror and Lens Equations?

[mikil100]

Homework Statement

In front of a spherical concave mirror of radius 39cm, you position and object of height 0.6cm somewhere along the principal axis. The resultant image has a height of 0.2cm, How far from the mirror is the object located?
What if this were a convex mirror with the same radius, and the same image and object height?

Homework Equations

1/f=1/Di+1/Do

M=Hi/Ho= -Di/Do

F=1/2R

The Attempt at a Solution

1/2R=19.5cm focal point

I have two equations with two unknowns (Di and Do). I used the equation Hi/Ho=-Di/Do to solve the equation for -Di, getting 0.2/0.6= 1/3. 1/3=-Di/Do, solving for Di I get -1/3Do=Di.

I then just plug this equation into the mirror equation

1/do+1/(-1/3do)=1/f... I bring the -3 from the denominator into the numerator

1/f is 2/39

1/d0-3/do=2/39

-2/do=2/39
do=-39cm

I follow the same process for a convex mirror but I get a positive answer with the same value of 39. I don't think a negative answer makes sense, and I am unsure of my sign usage... I find it odd that my object distance is the same as my mirrors radius.

Thank you in advance for the help.

 

[mfb]

1/do+1/(-1/3do)=1/f

Where does the minus sign come from?

do=-39cm

This would mean the object is right in the center of the sphere (or on the wrong side, depending on the sign convention). Can that be true?

 

[ehild]

Homework Equations

1/f=1/Di+1/Do

M=Hi/Ho= -Di/Do

F=1/2R

The Attempt at a Solution

1/2R=19.5cm focal point

I have two equations with two unknowns (Di and Do). I used the equation Hi/Ho=-Di/Do to solve the equation for -Di, getting 0.2/0.6= 1/3. 1/3=-Di/Do,

The image is smaller than the object. In case of a concave mirror, that means real image, which is upside-down, so Hi is negative, and Hi/Ho = -1/3 = -Di/Do.

 

[mikil100]

Where does the minus sign come from?

This would mean the object is right in the center of the sphere (or on the wrong side, depending on the sign convention). Can that be true?

Hi, thank you for the reply.

The negative sign in 1/(-1/3Do) is from this equation M=Hi/Ho= -Di/Do

Where Di is negative, getting Di on its own I have 0.2/0.6=-Di/Do----> 1/3*Do=-Di multiply both sides by -1 to get -1/3Do=Di

I then plugged the negative 1/3Do into 1/Di in the mirror equation. This negative sign is what is really tripping me up actually. When I do the same with the convex lense I get the same answer but the sign is switched in the final answer.

If the there was no negative # in 1/(1/3Do) then I will get 4/Do=1/F, which equals 78cm.

 

[ehild]

.

The negative sign in 1/(-1/3Do) is from this equation M=Hi/Ho= -Di/Do

Read my Post #3 . Hi is negative as it is an upside-down image.