An object placed 2cm in front of a converging lens of focal length 10cm produces a magnified image of 8cm high determine the position of the image and the size of the object
To determine the position of the image and the size of the object, we can use the magnification formula:
Magnification (M) = - (image height / object height) = (image distance / object distance)
Given data:
Focal length (f) = 10 cm
Object distance (u) = -2 cm
Image height = 8 cm
Since the object distance is negative, it indicates that the object is located on the same side as the incident light. The focal length is positive for a converging lens.
Using the magnification formula, we have:
M = - (image height / object height)
- (8 cm / object height) = (image distance / object distance)
Using the lens formula:
1/f = 1/v - 1/u
1/10 = 1/v + 1/2
1/v = 1/10 - 1/2
1/v = 1/10 - 5/10
1/v = -4/10
v = -2.5 cm
Since the image distance is negative, it indicates that the image is formed on the same side as the object (virtual image).
Now, we can calculate the magnification:
- (8 cm / object height) = (-2.5 cm / -2 cm)
8 / object height = 1.25
object height = 8 / 1.25
object height = 6.4 cm
Therefore, the position of the image is 2.5 cm on the same side of the object, and the size of the object is 6.4 cm.