Step-by-step explanation:
To draw a ray diagram for a converging lens, follow these steps:
1. Draw a horizontal line to represent the principal axis.
2. Place the lens on the principal axis with the convex side facing the object.
3. Mark the focal point (F) on the principal axis, which is 20 cm to the right of the lens (since it's a converging lens).
4. Place the object on the principal axis, 60 cm to the left of the lens.
5. Draw a ray from the top of the object parallel to the principal axis. This ray will pass through the focal point (F) after passing through the lens.
6. Draw a ray from the top of the object through the optical center of the lens. This ray will pass straight through without changing direction.
7. The point where these two rays intersect after refraction is the image of the object.
Now, to estimate the image distance:
Using the lens formula:
1/f = 1/u + 1/v
where f is the focal length, u is the object distance, and v is the image distance.
Given that f = 20 cm and u = -60 cm (since the object is placed 60 cm to the left of the lens), we can calculate v:
1/v = 1/20 + 1/(-60)
1/v = 1/20 - 1/60
1/v = (3 - 1) / 60
1/v = 2/60
Taking the reciprocal of both sides:
v = 60/2 cm = 30 cm
The positive sign indicates that the image is formed on the opposite side of the object (right side of the lens). The magnitude of the image distance is 30 cm, and its characteristics are:
- **Real Image:** The positive image distance indicates that the image is real, meaning it can be projected onto a screen.
- **Reduced Image:** Since the image distance (30 cm) is less than the object distance (60 cm), the image is smaller than the object.
- **Inverted Image:** The rays from the object converge after passing through the lens, forming an inverted image.