An object is located 27.6 cm to the left of a converging lens whose focal length is 46.5 cm. (a) Determine the image distance and (b) the magnification.
To determine the image distance and magnification, we can use the lens formula and magnification formula. Here are the steps to find the answers:
(a) Determining the image distance:
1. Use the lens formula, which states:
1/f = 1/di - 1/do
where f is the focal length, di is the image distance, and do is the object distance.
2. Substitute the given values:
f = 46.5 cm (given)
do = -27.6 cm (negative because the object is to the left of the lens)
3. Plug the values into the lens formula and solve for di:
1/46.5 = 1/di - 1/-27.6
Simplify:
1/46.5 = 1/di + 1/27.6
Use the common denominator 1271.4:
27.6/di = 1271.4 + 46.5
Now solve for di:
di = 27.6 / (1271.4 + 46.5)
di ≈ 0.0217 cm
Therefore, the image distance is approximately 0.0217 cm.
(b) Determining the magnification:
1. Use the formula for magnification, which is:
magnification (m) = -di/do
where di is the image distance and do is the object distance.
2. Substitute the given values:
di ≈ 0.0217 cm (calculated in part a)
do = -27.6 cm (given)
3. Plug the values into the magnification formula and solve for m:
m = -0.0217 / -27.6
Simplify:
m ≈ 0.000787
Therefore, the magnification is approximately 0.000787.