This unit is about how light changes direction when it bounces off a surface or passes into a new material, and how mirrors and lenses use that to form images. By the end, you should be able to draw ray diagrams, use Snell's law, and predict where an image forms, how big it is, and whether it is real or virtual.
Read the big ideas first, then work through each topic note and try the checkpoint question before you look at its answer.
In this unit, light is modeled as rays that travel in straight lines until they hit a boundary. At a boundary, light can both reflect back and refract into the new material. Curved mirrors and lenses can make rays from one point meet, or appear to come from one point, to form an image.
Honors Physics Unit 16 covers geometric optics in three parts. Reflection covers the law of reflection, plane mirrors, and concave and convex mirrors. Refraction covers the index of refraction, Snell's law, critical angle, and total internal reflection. Lenses covers converging and diverging lenses and the human eye. Across all three, you use ray diagrams, the mirror and thin lens equation , and the magnification equation to locate and describe images.
The law of reflection says , with both angles measured from the normal. A flat mirror gives a virtual, upright, same-size image. Curved mirrors focus or spread light, so they can make images that are larger, smaller, or flipped.
A material's index of refraction is , so a larger means slower light. Snell's law, , tells you how much the ray bends. If light tries to leave a slow material at too steep an angle, none of it gets out, and you get total internal reflection.
A converging lens can form a real image or a virtual one, depending on where the object sits relative to the focal point. For a real object, a diverging lens forms a virtual, upright, smaller image. The thin lens equation and the magnification equation give you the image location, size, and orientation.
A real image forms where rays actually converge, so you can project it on a screen. A virtual image forms where rays only seem to come from when you trace them backward, like the image behind a bathroom mirror. Ray diagrams show this geometry, and the equations turn it into numbers. Sign conventions keep track of which kind of image you have.
Light hitting a mirror leaves at the same angle it arrived, \theta_i = \theta_r.
Refraction is the change in direction of light as it crosses into a material where it moves at a different speed.
A lens refracts light at both of its surfaces to form an image.
Light hitting a mirror leaves at the same angle it arrived, . Measure both angles from the normal, the line perpendicular to the surface, and not from the surface itself. Smooth surfaces give specular reflection and a clear image. Rough surfaces like paper give diffuse reflection, which scatters light in many directions.
A plane mirror makes a virtual, upright image that is the same size as the object and as far behind the mirror as the object is in front. A concave mirror curves inward and focuses rays parallel to the principal axis near a focal point in front of it. A convex mirror curves outward and spreads rays, so it makes a virtual, upright, smaller image of a real object. For spherical mirrors and rays close to the principal axis, , where is positive for concave mirrors and negative for convex mirrors.
Use with positive for concave and negative for convex. A positive means a real image in front of the mirror. A negative means a virtual image behind it.
Worked example. A concave mirror has cm, and an object sits at cm. Then , so cm. Magnification is . The image is real, inverted, and half the object's height.
Try this question. A convex mirror has cm and an object is 12 cm away. Where is the image and what is it like? (Answer: , so cm. The image is virtual, 6 cm behind the mirror, upright, and half size since .)
| Mirror and object position | Image type | Orientation | Size |
|---|---|---|---|
| Plane mirror, any position | Virtual | Upright | Same size |
| Concave, object beyond C | Real | Inverted | Smaller |
| Concave, object between C and F | Real | Inverted | Larger |
| Concave, object inside F | Virtual | Upright | Larger |
| Convex, any position | Virtual | Upright | Smaller |
Refraction is the change in direction of light as it crosses into a material where it moves at a different speed. A ray entering along the normal changes speed but does not change direction. The index of refraction measures how much a material slows light. Some values are air at about 1.00, water at 1.33, glass at about 1.50, and diamond at 2.42. In water, light moves at m/s.
Light bends toward the normal when it enters a higher- material and away from the normal when it enters a lower- material. Snell's law gives the exact angle, .
Worked example. Light in air hits water at . Then , so and . The ray bent toward the normal because it entered a slower material.
Going the other way, from high to low , the refracted ray bends farther from the normal as you increase the incident angle. At the critical angle, the refracted ray skims along the surface at , so . For water to air, . Beyond that angle all the light reflects back. This is total internal reflection, which keeps light trapped inside fiber optic cables.
Try this question. What is the critical angle for light going from glass () into air? (Answer: , so .)
A lens refracts light at both of its surfaces to form an image. For a typical glass lens in air, a converging (convex) lens is thicker in the middle and brings rays parallel to the principal axis together near a focal point, so is positive. A diverging (concave) lens is thinner in the middle and spreads rays out, so is negative.
To draw a lens ray diagram, start with two rays. A ray parallel to the axis refracts through the far focal point, or for a diverging lens it seems to come from the near one. For a thin lens, a ray through the center goes approximately straight. The image is where the rays cross, or where their backward extensions cross.
The thin lens equation is , and magnification is . A positive means a real image on the far side of the lens. A negative means a virtual image on the same side as the object.
Worked example. A magnifying glass has cm, and you hold a bug cm away. Then , so cm. Magnification is . You see a virtual, upright image 4 times larger.
Your eye is a lens system. The cornea does most of the bending, and the lens changes shape to focus on near or far objects.
Try this question. An object sits 10 cm from a diverging lens with cm. Find the image. (Answer: , so cm. The image is virtual, on the object's side, upright, and half size since .)
| Lens and object position | Image type | Orientation | Everyday use |
|---|---|---|---|
| Converging, object beyond F | Real | Inverted | Camera, projector |
| Converging, object inside F | Virtual | Upright, enlarged | Magnifying glass |
| Diverging, any position | Virtual | Upright, smaller | Glasses for nearsightedness |
| Term | Definition |
|---|---|
| Law of reflection | The rule that the angle of incidence equals the angle of reflection, with both measured from the normal. |
| Snell's law | The equation $n_1 \sin\theta_1 = n_2 \sin\theta_2$ that relates the angles and indices of refraction at a boundary. |
| Focal length | The distance from a mirror or lens to its focal point, positive for converging devices and negative for diverging ones. |
| Real image | An image formed where light rays actually meet, which can be projected onto a screen. |
| Virtual image | An image located where rays only appear to come from, which cannot be projected onto a screen. |
| Magnification | The ratio $M = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$. A negative value means the image is inverted, and $|M| > 1$ means it is enlarged. |
| Thin lens equation | The relationship $\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$ that connects object distance, image distance, and focal length for a thin lens. The same relationship is called the mirror equation for a spherical mirror, using rays close to the principal axis. |
| Principal axis | The main symmetry axis of a mirror or lens. For a spherical mirror, it passes through the mirror's center of curvature. |
Problems often show the angle between the ray and the mirror or glass surface. Snell's law and the law of reflection both use angles from the normal. If you're given the angle to the surface, subtract it from before plugging it in.
A negative is a real answer. It means the image is virtual: behind the mirror, or on the same side of a lens as the object. Keep the sign and use it to describe the image instead of dropping it.
Light going from air into water or glass always refracts in, because it bends toward the normal and never reaches . Total internal reflection only happens going from higher to lower , and only past the critical angle.
A concave mirror converges light and has a positive . A concave lens diverges light and has a negative . To keep them straight, think about what each one does to parallel rays instead of relying on the shape name.