Just like we visualized ray paths with curved mirrors in earlier video, we will explore ray paths for lenses, especially a convex lens. Instead of a regular biconvex lens made from glass, we will use a biconvex profile made from acrylic. Different profiles of lenses made with acrylic enable us to study the ray path behaviour better. More on that later but lets cover the basics first.
When incident ray falls on the rectangular acrylic strip at 90 degrees, refracted ray extends the same path. Tilting the strip on either side, changes the path of light ray leaving the strip. This is due to a phenomenon called refraction we are all aware of . Light does not always change path when refraction occurs. Only when both mediums have different refractive index and light ray encounters medium change at an angle other than normal.Let us replace this strip with a triangle made from acrylic. This is a two dimensional version of the regular prism we are familiar with.
In this case, refracted light moves towards the wider side of the triangle. It is true even if we make it upside down or bring in another triangle. We can use two incident rays instead of one and understand the pattern better.
This formation of triangles is similar to the convex lens profile. In fact, a biconvex lens is a collection of many small prisms like this packed closely in a single piece.I have used different lenses of different radius of curvatures to analyze its behavior. Details on the design and related formula are discussed at the end. Refractive index of acrylic is 1.49 while that of water is 1.33 and that of glass is 1.5 approximately.We may not see perfect ray paths and exact focal length as per the formula but these approximations are good enough for our understanding. Let’s get started.
We will use graph paper for this activity. To avoid keeping the switch of laser light, pressed for a long duration, I have used a plastic bottle. Laser remains on as long as it is pressed inside the bottle.Eraser acts as a stand for laser.
We will place this graph paper on plastic containers. To make calculation easier, dashed lines are marked at a distance of 5 cm. Lasers placed on the left side act as a light source.Lens are placed here so that we can calculate distance easily.Rays coming from laser onto the convex lens are called incident rays.This is the principal axis.Placing a convex lens converges incoming parallel rays at a distance of 5 cm. This is also called focal length of the lens. This will change with change in medium as well. Like water instead of air. When an incident ray hits the lens, some of it is refracted while some of it is reflected back. Angle by which this happens is governed by the law of reflection.Let us use pieces from this matchstick for our analysis. We will call one matchstick as an object and another one as an image.
Let us place a convex lens here. Center of the lens is marked as C. Points F, marked in yellow are the focal points on each side while points marked 2f in red color, are at twice a distance of focal length from the center of the lens.As per this simbucket simulation , As per ray diagram, if an object is placed at 2F distance , that is twice the focal length, from the lens, we get a real , inverted image exactly at the same distance on the other side of the lens.
We can visualize three rules of refraction for a biconvex lens. Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.Focal length of the lens depends on the other medium as well. Let us place it in water. Small plastic container is made by folding a transparent plastic sheet. Soap solution is added to view the ray paths inside water.When placed inside the water, the focal length of this convex lens is more in water than in air.
Let us look at variations in type and size of lens. Observe how the path of refracted ray changes as I move the lens , perpendicular to incident rays.
Observe change in focal length, as lenses of different radius of curvature are placed.
This convex lens is of the same radius of curvature than the previous one but is thicker.
Focal length does not change significantly when thickness of lens varies for the same radius of curvature. These lenses have the same focal length but different thickness. Ideally, this thickness is very very small as compared to radius of curvature. But for our visualization purpose it should work.
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