An object is placed 20.0 cm to the left of a convex lens with a focal length of +8.0 cm. Where is the image of the object?
A)28 cm to the right of the lens
B)13 cm to the left of the lens
C)13 cm to the right of the lens
To determine the position of the image formed by a convex lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the image distance, and
- u is the object distance.
In this case, the object distance (u) is given as -20.0 cm (negative sign indicates that the object is on the left side of the lens) and the focal length (f) is given as +8.0 cm (positive sign indicates that it is a convex lens).
Substituting the values into the formula:
1/8 = 1/v - 1/-20
To solve for v, let's simplify the equation:
1/8 = (20 - v) / (-20v)
Now, cross-multiply:
-20v = 8(20 - v)
Expanding the expression:
-20v = 160 - 8v
Combine like terms:
-20v + 8v = 160
-12v = 160
Divide both sides by -12:
v = 160 / -12
Calculating the value:
v ≈ -13.333 cm
Since the value of v is negative, it indicates that the image formed by the convex lens is on the same side as the object, which means it is to the left of the lens. Therefore, the correct answer is:
B) 13 cm to the left of the lens