A Concave Lens and Image Formation
This article will discuss the formation of an image by a concave lens with a focal length of 15 cm when the image is located 10 cm from the lens.
Understanding Concave Lenses
Concave lenses, also known as diverging lenses, are thinner at the center than at the edges. They cause parallel rays of light to diverge, making them appear to originate from a single point called the focal point. The distance between the lens and the focal point is the focal length (f), which is negative for concave lenses.
Image Formation
Since the image is formed 10 cm from the lens, we know it's a virtual image. This is because concave lenses always form virtual images, which are upright and smaller than the object.
Using the Lens Formula
To determine the object distance (u), we can use the lens formula:
1/f = 1/v + 1/u
where:
- f = focal length (15 cm)
- v = image distance (10 cm)
- u = object distance
Substituting the values, we get:
1/-15 = 1/10 + 1/u
Solving for u, we get:
u = -6 cm
The negative sign indicates that the object is located on the same side of the lens as the virtual image.
Magnification
The magnification (M) of a lens is the ratio of the image height (h') to the object height (h):
M = h'/h = -v/u
Substituting the values, we get:
M = -10/-6 = 1.67
This indicates that the image is 1.67 times larger than the object.
Conclusion
Therefore, when a concave lens with a focal length of 15 cm forms an image 10 cm from the lens, the object is located 6 cm from the lens. The image is virtual, upright, and 1.67 times larger than the object.
