Calculating the Focal Length of a Concave Mirror

[itryphysics]

concave mirror!

Homework Statement

The real image produced by a concave mirror is found to be 0.756 times the size of the object. If the distance from the mirror to the screen on which the image appears is 0.764 m , what is the focal length of the mirror?

Homework Equations

(a) 1 /d_o + 1/d_i = 1/f

(b) image height / object height=m = - d_i/d_o

(c) - object height / image height = d_o / d_i

The Attempt at a Solution

m= 0.756 = -hi / ho

so to use equation "c"

i inverted --- > -1/0.756
then set it euqal to rest of the equation so --> -1/.756 = do / .764
do= -1.01058 m

then i used equation "a"

(1/-1.01058) + (1/.764) = 1/f and solved for f

Answer was Wrong. Please tell me what I need to do. Thank you!

 

[rl.bhat]

I got the answer 0.435 m. Is it correct? If so check your sign convention.

 

[nlightner]

I would first check the calculations and make sure all units are consistent. It appears that you have used meters for distance, but have not included units for the image and object heights. Also, for equation (c), the negative sign in front of the object height should be included.

Assuming the calculations are correct, the next step would be to consider the focal length equation (a). This equation states that the sum of the inverse of the object distance (do) and the inverse of the image distance (di) is equal to the inverse of the focal length (f). Therefore, if we have values for do and di, we can solve for f.

In this case, we have do = -1.01058 m and di = 0.764 m. Plugging these values into equation (a), we get:

(1/-1.01058) + (1/0.764) = 1/f

Simplifying, we get:

-0.9895 + 1.3099 = 1/f

0.3204 = 1/f

f = 1/0.3204 = 3.121 m

Therefore, the focal length of the concave mirror is approximately 3.121 m.

I would also consider the accuracy and precision of the measurements used in this calculation, and make sure to report the answer with the appropriate number of significant figures. I hope this helps!