Step-by-step explanation:
To draw a ray diagram for a concave lens, follow these steps:
1. Draw a horizontal line to represent the principal axis.
2. Place the lens on the principal axis with the concave side facing the object.
3. Mark the focal point (F) on the principal axis, which is 20 cm to the left of the lens.
4. Place the object on the principal axis, 10 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 refract through the focal point 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 (since it's a concave lens) and u = -10 cm (since the object is placed 10 cm to the left of the lens), we can calculate v:
1/v = 1/(-20) + 1/(-10)
1/v = (-1/20) + (-1/10)
1/v = (-1/20) - (2/20)
1/v = -3/20
Taking the reciprocal of both sides:
v = -20/3 cm ≈ -6.67 cm
The negative sign indicates that the image is virtual and formed on the same side as the object (left side of the lens). The magnitude of the image distance is 6.67 cm, and its characteristics are:
- **Virtual Image:** The negative image distance indicates that the image is virtual, meaning it is formed on the same side as the object and cannot be projected onto a screen.
- **Enlarged Image:** Since the image distance (-6.67 cm) is greater than the object distance (-10 cm), the image is larger than the object.
- **Upright Image:** The rays from the object diverge after passing through the lens, forming an upright image.