3. Mirrors and Lenses

1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

• Applies to concave and convex mirrors
• Sign convention: distances positive in direction of light

The mirror equation relates the focal length (f) of a mirror to the distance of the object (u) and the distance of the image (v). It is expressed as $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$. This equation can be used for both concave and convex mirrors. The sign convention states that the distances are considered positive when they are in the direction of the incoming light.

Imagine a flashlight shining on a mirror. The distance from the flashlight (object) to the mirror (u) and the distance from the mirror to the reflected image (v) can be measured. The mirror helps us find these relationships just like how your reflection in the mirror behaves at a certain focal point.

1f=1v−1u\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

• For convex (converging) and concave (diverging) lenses

The lens formula is similar to the mirror equation but applies to lenses. It is given by $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$. This equation can be used for both convex lenses, which converge light, and concave lenses, which diverge light. Here, the focal length (f) is associated with how the lens bends the light, and u and v are still the object and image distances respectively.

Think of a magnifying glass. If you're reading a book and want to use a magnifying glass (convex lens) to see it more clearly, you would notice that as you move it closer or further away, the image appears larger or smaller depending on its position relative to the focal length.

For mirrors: m=−vum = \frac{-v}{u} For lenses: m=vu m = \frac{v}{u}

Magnification (m) describes how much larger or smaller an image appears compared to the original object. For mirrors, magnification can be calculated with $m = \frac{-v}{u}$ where v is the image distance and u is the object distance. For lenses, the formula changes slightly to $m = \frac{v}{u}$. This difference arises from the way lenses and mirrors produce images — mirrors often produce an inverted image, while lenses can enhance the size of an image.

Consider a makeup mirror that is concave and makes you look bigger. The magnification would be calculated using the mirror formula. If you were instead looking through a camera lens, the lens would determine how much the image is magnified based on its distance from you.

● Microscope: Uses two convex lenses (objective + eyepiece) ● Telescope: Distant object lens + magnifier ● Human Eye: Variable focal length lens system

Optical instruments use lenses or mirrors to manipulate light for different purposes. For example, a microscope employs two converging (convex) lenses: one for capturing the image and another for viewing it (eyepiece). A telescope operates similarly by using one lens to focus distant light onto another lens that magnifies the image. The human eye acts as a natural lens system, where the lens can change shape to focus on nearby or distant objects, functioning like an adjustable optical device.

Think about how you use a telescope to watch stars at night or a microscope to observe tiny microbes in a drop of water. Just like toggling between lenses, your eye can focus on objects at varying distances, allowing you to see the world clearly whether it's a close-up or far away.

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