Final answer:
To find the position of the image formed by a lens with a focal length of 10 cm held at a distance of 5 cm from the palm, the lens formula gives an image position of approximately 3.33 cm, which is real and inverted with two-thirds the size of the object.
Step-by-step explanation:
Rishi went to a palmist who used a lens with a focal length of 10 cm to view his palm.
To find the image position using the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance, we substitute the given values:
f = +10 cm (convex lens), do = -5 cm (object distance is considered negative as the object is real and it lies on the same side as the light is coming from).
Using the lens formula, we rearrange the terms to solve for
di: 1/di = 1/f - 1/do
= 1/10 - (-1/5)
= 1/10 + 1/5
= 1/10 + 2/10
= 3/10.
Therefore, di = 10/3 cm, which means the image is formed at a distance of 10/3 cm or approximately 3.33 cm on the same side as the object, since the image distance is positive.
This indicates that the image is real and inverted.
The magnification (m) of the image is given by the ratio of the image distance to the object distance (m = -di/do). Therefore, m = -10/3 cm / -5 cm
= 10/3 cm / 5 cm
= 2/3.
This means the image is two-thirds the size of the object and is inverted.