# Geometric Optics: Reflection and Refraction

Physics I · Principles of Electromagnetism and Optics · https://tryals.app/learn/physics-i/geometric-optics-reflection-and-refraction

## Bending Light at Boundaries

A straw in a glass of water looks broken because your brain traces bent light rays backwards to a false location. All of geometric optics follows rays reflecting and refracting at surfaces to find where images appear.

When light strikes a boundary, it follows two core rules:

**Law of reflection**: $\theta_i = \theta_r$, where angles are measured from the surface normal.

**Snell's law of refraction**: $n_1\sin\theta_1 = n_2\sin\theta_2$, where **refractive index** $n = c/v$ measures how much a medium slows light down.

**Total internal reflection** occurs when light travels from a denser medium ($n_1 > n_2$) at an angle exceeding the **critical angle** $\theta_c = \arcsin(n_2 / n_1)$.

> **Common pitfall**: Total internal reflection happens only when light leaves a slower, denser medium for a faster one. Going from air into glass, light always refracts regardless of the angle.

## Lenses, Mirrors, and Images

Lenses and spherical mirrors locate images using standard equations and sign conventions. The **thin lens equation** and the **mirror equation** share the same mathematical form:

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

where $f = R/2$ for spherical mirrors. **Magnification** is given by $m = -d_i / d_o$.

| Property | Positive Value | Negative Value |
| --- | --- | --- |
| Image Type | **Real** ($d_i > 0$, opposite side) | **Virtual** ($d_i < 0$, same side) |
| Orientation | **Upright** ($m > 0$) | **Inverted** ($m < 0$) |

> **Tip**: Always draw a ray diagram with at least two principal rays to catch sign errors and build physical intuition.

## Practice questions

5 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Which are properties of a real image formed by a converging lens?

A. Inverted
B. Always the same size as the object
C. Formed when d_o > f
D. Can be projected on a screen

**Answer:** A. Inverted; C. Formed when d_o > f; D. Can be projected on a screen

**Why:** Real images are inverted and projectable; size depends on d_o relative to 2f.

Page: https://tryals.app/practice/physics-i/geometric-optics-reflection-and-refraction/which-are-properties-of-a-real-image-formed-by-a-converging-lens

### 2. A fisherman looks down at a fish under the water’s surface. Because light **bends** when leaving the water, where does the fish appear compared to where it really is?

A. Shallower than it really is
B. Exactly where it is, refraction only blurs it
C. Displaced sideways but at the true depth
D. Deeper than it really is

**Answer:** A. Shallower than it really is

**Why:** Rays from the fish bend away from the normal at the surface; extended backwards, they intersect above the true position. The fish sits deeper than it looks, which is why spear fishers aim **below** the image.

Page: https://tryals.app/practice/physics-i/geometric-optics-reflection-and-refraction/a-fisherman-looks-down-at-a-fish-under-the-waters-surface-because

### 3. Light enters glass, where it travels at $2\times10^{8}$ m/s instead of $3\times10^{8}$ m/s. Estimate the **index of refraction** of this glass.

**Answer:** 1.5 (within ±0.1)

**Why:** $n = 1.5$, typical window glass. All of refraction follows from this slowdown: wavefronts entering at an angle pivot like a marching band stepping onto mud, the side that slows first swings the line around.

Page: https://tryals.app/practice/physics-i/geometric-optics-reflection-and-refraction/light-enters-glass-where-it-travels-at-2-10-m-s-instead-of-3-10

### 4. The angle of incidence equals the angle of refraction when light passes into a denser medium.

**Answer:** False

**Why:** False. That is the law of **reflection**. Refraction bends the ray toward the normal on entering a denser medium, following Snell's law $n_1\sin\theta_1 = n_2\sin\theta_2$, the angles are equal only at normal incidence or when the indices match.

Page: https://tryals.app/practice/physics-i/geometric-optics-reflection-and-refraction/the-angle-of-incidence-equals-the-angle-of-refraction-when-light

### 5. Light bends toward the normal entering glass and away from it leaving. What explains both?

A. Glass attracts light, pulling it toward the normal
B. The two cases obey different laws, reflection and refraction
C. The frequency of the light changes at the boundary
D. Light travels more slowly in the denser medium

**Answer:** D. Light travels more slowly in the denser medium

**Why:** One mechanism, two directions. This is also why total internal reflection happens only going from slow to fast, the refracted ray would need a sine greater than one.

Page: https://tryals.app/practice/physics-i/geometric-optics-reflection-and-refraction/light-bends-toward-the-normal-entering-glass-and-away-from-it