a convex lens of an optical instrument needs to form an inverted image that is 4 times smaller than the object. how far from the lens should the object be placed?
Answer: behind the double focal point. can someone explain this to me please?
i have a similar question. A CONCAVE lens of an optical instrument needs to form an inverted image that is 4 times smaller than the object. how far from the lens should the object be placed?
Answer: this image will never be formed regardless of the placement of the object. why?
To understand why the object should be placed behind the double focal point of a convex lens in order to form an inverted image that is 4 times smaller, we need to understand a few basic principles of convex lenses.
1. Convex Lens: A convex lens is thicker at the center than at the edges and is often referred to as converging lens. It can converge the incoming light rays and is commonly used in magnifying glasses, cameras, and other optical instruments.
2. Focal Point: A convex lens has two focal points - one on each side of the lens. These focal points are symmetrically located at equal distances from the center of the lens.
3. Image Formation by a Convex Lens: When an object is placed in front of a convex lens, the rays of light emitted from the object bend or refract as they pass through the lens. The point at which these refracted rays converge or intersect is where the image is formed.
Now, let's consider the situation where the convex lens needs to form an inverted image that is 4 times smaller than the object. Placing the object behind the double focal point of a convex lens ensures that the image formed will be inverted and smaller.
Here's the explanation:
1. Positioning the Object: When the object is placed behind the double focal point, the rays of light emitted from the object are refracted by the convex lens and converge to form an image. Placing the object at this position ensures that the image will be inverted.
2. Image Size: In this case, the objective is to form an image that is 4 times smaller than the object. To achieve this, the distance between the object and the lens should be larger than the distance between the lens and the image. By placing the object behind the double focal point, the image formed will be smaller.
Now, let's consider the situation for a concave lens that needs to form an inverted image that is 4 times smaller than the object.
A concave lens is thinner at the center than at the edges and is commonly referred to as a diverging lens. It diverges incoming light rays instead of converging them. Due to the characteristics of a concave lens, it's not possible to form a real image that is inverted and smaller than the object, regardless of where the object is placed.
Here's the explanation:
1. Divergence of Light: When light passes through a concave lens, the rays of light diverge or spread out instead of converging at a focal point. This divergence prevents the formation of a real image on the opposite side of the lens.
2. Virtual Image Formation: In the case of a concave lens, the image formed is a virtual image. A virtual image is one that cannot be projected onto a screen as it is formed by extrapolating the rays of light backward. This type of image does not have a physical presence and cannot be captured.
Therefore, regardless of the placement of the object, it is not possible to form an inverted image that is 4 times smaller using a concave lens.