An object that is 31 cm in front of a convex mirror has an image located 16 cm behind the mirror. How far behind the mirror is the image located when the object is 24 cm in front of the mirror?
do I use the formula
1/f = 1/di + 1/do??
please help
yes, that is the right formula. Observe the sign conventions in your text.
Yes, you are correct. The formula you mentioned, 1/f = 1/di + 1/do, is the correct formula to use to find the final image distance.
In this formula:
- f represents the focal length of the convex mirror
- di represents the image distance
- do represents the object distance
To find the final image distance when the object is 24 cm in front of the mirror, you can use the given information and the formula:
Given:
do = 31 cm
di = -16 cm (negative sign indicates a virtual image)
Plugging in the values into the formula:
1/f = 1/di + 1/do
1/f = 1/-16 + 1/31
To simplify, you can find a common denominator:
1/f = (-31 + 16)/(31 * -16)
1/f = (-15)/(31 * -16)
1/f = 15/496
Now, you can solve for f by taking the reciprocal of both sides:
f = 496/15
So, the focal length of the convex mirror is approximately 33.07 cm.
Now that you have the focal length, you can plug in the new object distance (do = 24 cm) into the formula to find the new image distance (di):
1/f = 1/di + 1/do
1/33.07 = 1/di + 1/24
Again, finding a common denominator:
1/33.07 = (24 + di)/(24 * di)
1/33.07 = (24 + di)/(576)
To isolate di, multiply both sides by 576:
di = (576 * 1) / (33.07 * 33.07)
di = 576 / 1094.44
di ≈ 0.527 cm
Therefore, when the object is 24 cm in front of the mirror, the image distance is approximately 0.527 cm behind the mirror.
Remember to double-check your calculations and round your final answer appropriately based on significant figures or instructions provided.