a converging lens has a focal length of 10.0 cm. find the location of the image for object distances of a) 40.0cm b) the magnification
1/f=1/di+1/do
You need to review the rules for signs.
To find the location of the image formed by a converging lens, we can use the lens formula:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens,
- do is the object distance (distance of the object from the lens), and
- di is the image distance (distance of the image from the lens).
a) For an object distance of 40.0 cm and a focal length of 10.0 cm, we can substitute the values into the lens formula:
1/10 = 1/40 + 1/di
Simplifying this equation, we get:
1/di = 1/10 - 1/40
= 4/40 - 1/40
= 3/40
To find the value of di, we take the reciprocal of both sides:
di = 40/3
Therefore, the location of the image for an object distance of 40.0 cm is approximately 13.33 cm.
b) To find the magnification of the image formed by a lens, we can use the formula:
magnification (m) = -di/do
Where:
- di is the image distance (which we already found in part a),
- do is the object distance (given as 40.0 cm in this case).
Substituting the known values, we get:
m = - (40/3) / (40)
= -1/3
Therefore, the magnification of the image is -1/3. This indicates that the image is inverted and smaller than the object.