Types of Lenses
Two Main Types: Lenses come in two main categories based on how they bend light and their shapes. These are called convex lenses, which bend light rays inward (converging), and concave lenses, which bend light rays outward (diverging).
Convex Lenses: A convex lens is thicker in the middle than at the edges. When light rays that are parallel hit the lens, they bend inward and meet at a point called the focal point.
Other Names for Convex: Convex lenses are also known as converging lenses because they bring light rays together. Some people also call them positive lenses because of the way they focus light.
Types of Convex Lenses: There are several shapes of convex lenses, such as:
- Double convex (biconvex): curved outward on both sides,
- Plano-convex: one side is flat, and the other is curved outward,
- Meniscus convex: both sides are curved, but one side is less curved than the other.
Concave Lenses: A concave lens is thinner in the middle and thicker at the edges. When parallel light rays enter the lens, they spread out, or diverge, as if they came from a single point.
Other Names for Concave: Concave lenses are also called diverging lenses because they spread light rays apart. Another term for them is negative lenses because they do not focus light like convex lenses do.
Types of Concave Lenses: These include:
- Double concave (biconcave): curved inward on both sides,
- Plano-concave: one side is flat, and the other is curved inward,
- Meniscus concave: both sides are curved inward but with different curvatures.
Key Terms Related to Lenses
Principal Axis: This is a perfectly straight line that passes through the middle of the lens, also known as the optical center, and it stands at a right angle (90°) to the surface of the lens on both sides. It acts as a guide or reference line that helps us understand how light travels through the lens and where the rays will go after passing through.
Optical Centre (O): The optical center is the exact center point of the lens. When light rays go through this point, they do not bend or change direction. Instead, they keep going in a straight line, which makes it an important part of lens diagrams.
Focal Point (F): For convex lenses, the focal point is the place where light rays that are coming in straight and parallel to the principal axis bend inward and meet after passing through the lens. For concave lenses, it’s a point on the same side as the object where the light rays appear to come from after they spread out or diverge. In diagrams, the focal point helps show where the image will form.
Focal Point Type: A convex lens has a real focal point because the bent light rays actually meet at that point. A concave lens has a virtual focal point because the light rays don’t really meet there—they just appear to come from that spot when we trace them backward.
Focal Length (f): This is the distance between the optical center of the lens and its focal point. For convex lenses, the focal length is positive because the rays really meet at a point. For concave lenses, it is negative because the rays only seem to come from the focal point and don’t actually meet there.
Object Distance (u): This is how far the object being observed is placed in front of the lens, measured from the optical center. Knowing the object distance helps us figure out where and what kind of image will be formed—whether it’s big or small, upright or upside-down.
Image Distance (v): This is how far the image appears from the lens’s optical center. The image distance depends on how far the object is and which type of lens is being used (convex or concave). This helps us find out if the image is real or virtual.
Radius of Curvature (R): This tells us how curved the surface of the lens is. It is equal to twice the focal length, and the formula used to find it is R = 2f. If the radius is large, the lens is flatter. If it’s small, the lens is more curved.
Ray Diagrams for Convex Lenses
Parallel Ray: When a light ray comes in straight and parallel to the principal axis, it bends after going through the lens and passes through the focal point on the opposite side. This ray helps us find where the image will be.
Optical Centre Ray: If a ray of light passes straight through the optical center of the lens, it keeps moving in a straight line and does not bend at all. This makes it easy to draw in diagrams.
Focal Ray: If a light ray travels toward the focal point on the object’s side of the lens, after passing through the lens, it bends and moves straight and parallel to the principal axis. This is another important ray used to locate the image.
Ray Diagrams for Concave Lenses
Parallel Ray in Concave: A ray that enters the concave lens in a direction parallel to the principal axis will bend outward (diverge) after going through the lens. If we trace it back in a straight line, it looks like it came from the focal point on the same side as the object.
Optical Centre Ray in Concave: A ray that travels through the optical center of a concave lens does not bend. It goes in a straight path just like in a convex lens, making it easy to include in ray diagrams.
Focal Ray in Concave: A ray that seems to be heading toward the focal point on the far side of the lens will bend when it passes through the lens. After it exits, it moves parallel to the principal axis. This ray helps us predict how the image will appear.
Characteristics of Images Formed by Lenses
Real Image: A real image is formed when light rays actually come together and meet after passing through a lens. Because the light rays truly intersect at a point, this image can be captured or projected onto a screen, like how a projector displays a movie.
Virtual Image: A virtual image is created when the light rays don’t really meet but only seem to do so when traced backward. The image appears in your eyes but doesn’t exist in space, so you can’t catch it on a screen. It’s like seeing your reflection in a mirror—your face looks real but you can’t touch or project it.
Upright Image: An upright image appears the same way up as the actual object. It is not flipped over, so the top of the object stays at the top in the image too. This makes it easier to recognize, just like looking at your face straight in a mirror.
Inverted Image: An inverted image is one that appears upside down when compared to the original object. The top becomes the bottom and the bottom becomes the top. This usually happens with real images formed by convex lenses.
Magnified Image: A magnified image appears larger than the real object. This means the image looks stretched or zoomed in, like when you use a magnifying glass to look at something tiny and it appears bigger than its actual size.
Diminished Image: A diminished image is smaller than the original object. The image looks shrunken or reduced, as if you were seeing the object from far away.
Same Size Image: A same-size image has exactly the same height and width as the original object. It’s a copy that looks neither bigger nor smaller.
Image Location (Convex): With a convex lens, where the image appears depends on where the object is placed. Sometimes the image shows up on the opposite side of the lens, and other times it appears on the same side. This depends on how close or far the object is from the lens.
Image Location (Concave): For concave lenses, no matter where the object is placed, the image always forms on the same side of the lens as the object. It never moves to the other side because the light rays spread out (diverge) after passing through the lens.
Image Characteristics for Convex Lenses
Object at Infinity (u = ∞): When the object is placed extremely far away from the lens—so far that the rays arriving at the lens are almost perfectly parallel—the image will form right at the focal point. This image is very small, which we call diminished, it is upside down (inverted), and it is real, meaning it can be projected onto a screen.
Object Beyond 2f (u > 2f): If the object is located farther than twice the focal length away from the lens, the image that forms will be real and inverted. It will also be smaller than the object and will appear between the focal point (f) and twice the focal length (2f) on the other side of the lens.
Object at 2f (u = 2f): When the object is placed exactly at a distance of two focal lengths from the lens, the image formed will be the same size as the object. It will still be real and inverted and will appear at 2f on the other side of the lens.
Object Between f and 2f (f < u < 2f): If the object is between the focal point and twice the focal length, the image formed will be bigger than the object (magnified), real, and inverted. It will appear beyond 2f on the other side of the lens.
Object at f (u = f): If the object is placed exactly at the focal point, no image forms on the screen. This is because the rays of light exit the lens parallel to each other and never meet. In theory, the image would be at infinity, too far away to be seen.
Object Between f and O (u < f): If the object is very close to the lens, between the focal point and the optical center, the image formed will be virtual (not real), upright (not upside down), magnified (larger than the object), and it will appear on the same side of the lens as the object.
Image Characteristics for Concave Lenses
Universal Traits: A concave lens always creates the same kind of image no matter how far or close the object is. The image is always virtual (can’t be projected on a screen), upright (standing the same way as the object), and diminished (smaller than the object).
Location of Image: The image formed by a concave lens will always appear on the same side of the lens as the object. This happens because the light rays spread out (diverge) after passing through the lens, and our eyes trace them back to a point on the object’s side.
Linear Magnification (m)
Definition of m: Magnification tells us how much larger or smaller the image is when compared to the object. It helps us know whether the image is zoomed in or shrunk. We calculate magnification by dividing the height of the image by the height of the object, or we can also divide the image distance by the object distance.
Formula for m: The formula used to calculate magnification is: m = hᵢ / h₀ = v / u, where hᵢ is the height of the image, h₀ is the height of the object, v is the distance from the lens to the image, and u is the distance from the lens to the object.
Magnification > 1: If the value of magnification is more than 1, this means the image is larger than the object. We call this a magnified image.
Magnification < 1: If the magnification value is less than 1, the image is smaller than the object. This kind of image is called diminished.
Magnification = 1: If the magnification is exactly 1, the image and the object are the same size. There is no enlargement or reduction.
Sign of m: The sign in front of the magnification value tells us the image’s orientation. If the magnification is positive, the image is upright. If it is negative, the image is inverted (flipped upside down).