Images from Lenses and Mirrors

Images from Lenses and Mirrors: AP Physics 2 Study Guide

Welcome to the magical world of optics, where mirrors do more than just show you a bad hair day and lenses help turn blurry visions into sharp images. Whether you’re a fan of those giant, concave beauty mirrors or just curious about the physics of photons bouncing around, buckle up! We’re diving deep into the land of reflections, refractions, and a little something called ray tracing. 🕶️

Let’s start with the simplest kind of mirror: plane mirrors. Plane mirrors are as flat as your attempts at telling Dad jokes, but they do some pretty interesting work with light.

When you look at an object in a flat mirror, light reflected off the object hits the mirror and then bounces back into your eyes. The direction of this reflected light determines where you perceive the image to be.

• When you stare at your reflection, it appears that the image is behind the mirror at the same distance as you are in front of it. It’s like magic, but it’s just physics, I promise.
• The image is neither shrunken down to make you look mini nor enlarged to make you look like a giant—it’s the same size as the real you.
• Most importantly, the image in a plane mirror is virtual (meaning the light rays don’t actually converge at the location of the image) and upright (thank goodness, or you’d get dizzy).

Now, things get a bit curvy with concave and convex mirrors. Imagine slicing a shiny, disco ball in half; you now have two spherical mirrors with very different jobs.

Concave Mirrors

Concave mirrors curve inward, just like your stomach when you smell freshly baked cookies. These mirrors can focus light to a point (the focal point), and they follow some special rules:

1. Light rays parallel to the principal axis reflect through the focal point.
2. Light rays passing through the focal point reflect parallel to the principal axis.
3. Rays passing through the vertex (the center of the mirror) reflect at equal angles to the principal axis.

Convex Mirrors

Convex mirrors curve outward, like the belly of a well-fed raccoon. They spread light rays apart and also follow some rules:

1. Light rays parallel to the principal axis appear to come from the focal point behind the mirror.
2. Light rays aimed at the focal point reflect parallel to the principal axis.
3. Rays passing through the vertex reflect at equal angles.

And just like that, concave mirrors make real images (which means the light actually converges), while convex mirrors always produce virtual images that are upright and smaller. Handy for security mirrors in stores watching out for your sneaky snacking!

Ray tracing helps you find out where the image will form. You draw the object, the mirror, and a couple of light rays. The intersection of the reflected rays is where your image appears.

For concave mirrors:

• Parallel rays reflect through the focal point.
• Rays through the focal point reflect parallel to the axis.

For convex mirrors:

• Parallel rays reflect as if they came from the focal point.

It gets even more fun with lenses, which bend light instead of reflecting it.

Converging Lenses (Convex)

Convex lenses are thicker in the middle and bring parallel light rays together to a point (converge them). It’s like focusing all your thoughts on getting that last slice of pizza.

Diverging Lenses (Concave)

Concave lenses are thinner in the middle and spread light rays apart (diverge them). Like trying to keep your room tidy—everything goes everywhere.

For lenses, draw three rays from the top of the object:

1. A ray parallel to the axis refracts through the focal point.
2. A ray through the center of the lens passes straight.
3. A ray through the focal point refracts parallel to the principal axis.

You can use the mirror/lens equations for quick calculations:

1/f = 1/do + 1/di

• Converging mirrors/lenses (concave mirrors and convex lenses) have positive focal lengths.
• Diverging mirrors/lenses (convex mirrors and concave lenses) have negative focal lengths.

The magnification equation is: M = -di/do = hi/ho

• Real images are inverted.
• Virtual images are upright.

Here’s where the rubber meets the road! Try solving these problems to test your understanding.

1. A plane mirror produces an image that is: E) Virtual, upright, and the same size as the object.
2. An object at 0.20 meters from a converging lens with a 0.15-meter focal length: C) Real, inverted, larger.
3. Direction of light after passing through a lens parallel to the optic axis: C) It bends through the focal point.
4. Light traveling from glass (n=1.5) to air (n=1.0) at 60 degrees: E) Total internal reflection if the incident angle is above the critical angle.
5. Real image distance for a concave mirror with a 10 cm radius of curvature: C) 10 cm.
6. Diverging lens image characteristics: B) Virtual, smaller than the object, and upright.

So, there you have it! The world of optics can be as fascinating as it is practical. Whether you’re looking into a vanity mirror or analyzing light through a telescope, understanding how mirrors and lenses work can shed light (pun intended) on the many ways we manipulate and understand our visual world. Happy studying, and may your reflections always be accurate and your lenses always be in focus! 📸