An object place 5cm in front of a converging lens of focal lenght 10cm produces a magnified image 8cm.find the size and the position of the image
To find the size and position of the image formed by a converging lens, we can use the lens formula and the magnification formula. Here are the steps to find the solution:
1. Determine the known values:
- Object distance (u) = -5 cm (since the object is placed in front of the lens, we take the value as negative)
- Focal length (f) = +10 cm (converging lens has a positive focal length)
- Image distance (v) = ? (unknown)
- Magnification (m) = 8 cm (given)
2. Use the lens formula to find the image distance (v):
The lens formula is: 1/f = 1/v - 1/u
Plugging in the known values, we have: 1/10 = 1/v - 1/(-5)
Simplifying the equation: 1/10 = 1/v + 1/5
Adding the fractions, we get: 1/10 = (1 + 2)/v
Combining like terms, we have: 1/10 = 3/v
Inverting both sides of the equation, we get: v/3 = 10
Solving for v, we have: v = 10 * 3 = 30 cm
Therefore, the image distance (v) is 30 cm.
3. Use the magnification equation to find the size of the image:
The magnification formula is: m = -v/u
Plugging in the known values, we have: 8 = -30/(-5)
Simplifying the equation: 8 = 6
Since the calculated magnification is not equal to the given magnification, there may be an error in the given values or a mistake in the question.
In conclusion, with the given information, it seems there might be some inconsistency between the given magnification and the values provided for the object distance and image distance. Double-check the given values to ensure accuracy in solving for the size and position of the image.