Concave Mirror and objects distance

[sheri1987]

Homework Statement

A concave mirror (f = 44 cm) produces an image whose distance from the mirror is one-fourth the object distance.

(a) Determine the object distance.
cm

(b) Determine the (positive) image distance.
cm

Homework Equations

1/do +1/di =1/f do=object distance and di=image distance

The Attempt at a Solution

Since there are two unknowns I thought I could change the equation to 1/do + 1/4do = 1/f...and solve but this wasn't turning out right? am I going about this the wrong way?

 

[Snazzy]

Is 1/4do equal to (1/4)do or 1/(4do)? In any case, if the image distance is one-fourth the object distance, does that mean that di = 4do?

 

[Moetasim]

I would approach this problem by using the equation for concave mirrors, 1/do + 1/di = 1/f, where do is the object distance, di is the image distance, and f is the focal length. Since we are given the focal length (f = 44 cm) and the relationship between di and do (di = 1/4do), we can substitute these values into the equation and solve for do.

1/do + 1/(1/4do) = 1/f

Multiplying both sides by do:

1 + 4 = do/f

5 = do/f

Multiplying both sides by f:

5f = do

Substituting the given value for f (f = 44 cm):

5 x 44 cm = do

Therefore, the object distance is 220 cm.

To determine the image distance, we can use the relationship given in the problem (di = 1/4do) and substitute the value we just found for do:

di = 1/4(220 cm)

di = 55 cm

Therefore, the image distance is 55 cm.

In summary, the object distance is 220 cm and the image distance is 55 cm. This means that the image is one-fourth the size of the object and is located 55 cm away from the concave mirror.