A converging lens is 50cm away from the object. if the distance of the image from the object is 120cm and greater than four times the focal length of the lens, what is the focal length of the said lens?
120cm
To find the focal length of a converging 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 distance of the image from the lens
- u is the distance of the object from the lens
Given:
- The distance of the object from the lens (u) is 50 cm
- The distance of the image from the lens (v) is 120 cm
Substituting the given values into the lens formula:
1/f = 1/120 - 1/50
Now, let's find the common denominator:
1/f = (50 - 120) / (120 * 50)
Simplify the numerator:
1/f = (-70) / (6000)
Now, invert both sides to isolate 'f':
f = 6000 / (-70)
Simplify:
f = -85.71 cm
Since focal lengths cannot be negative, we take the absolute value:
f ≈ 85.71 cm
Therefore, the focal length of the converging lens is approximately 85.71 cm.