---
title: "Shadows and Eclipses"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 50
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/50-shadows-and-eclipses
---

# Chapter 50 — Shadows and Eclipses

Once or twice in a lifetime, for a few minutes, day becomes night: the Sun’s disc goes black behind the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) and [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) appear at noon. Ancient peoples read doom in it; you will read geometry. An eclipse is nothing but a [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) — the largest [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) you will ever stand in — and your ruler-and-ray toolkit is exactly what it obeys.

## 50.1 Shadows from honest lamps

**Proposition 50.1 (Umbra and penumbra).**

A *point-like* source throws a single, sharp-edged [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow). A *broad* source — a frosted globe, the Sun’s whole disc — throws a two-part [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow):

1. the *umbra* : the region reached by [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) from *no* part of the source — full darkness;
2. the *penumbra* : the fringe reached by [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) from *part* of the source only — half [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) , fading outward.

From inside the [umbra](#prop-g7-shadows-eclipses-umbra), the source is entirely hidden; from the [penumbra](#prop-g7-shadows-eclipses-umbra), partly hidden — peeking over the blocker’s edge.

**Method 50.2 (Constructing the two shadows).**

For a broad source, rays from its *edges* rule the map:

1. draw rays from the source’s top edge grazing the blocker’s two sides, and the same from the bottom edge;
2. the region behind the blocker that *both* edges’ rays miss is the [umbra](#prop-g7-shadows-eclipses-umbra) ;
3. the flanking regions missed by one edge but reached by the other are the [penumbra](#prop-g7-shadows-eclipses-umbra) ;
4. where all rays arrive, full [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) .

The [umbra](#prop-g7-shadows-eclipses-umbra) of a round blocker is a cone — and whether that cone reaches a given screen decides everything about eclipses.

![A broad source’s double shadow: the umbra, blind to the whole source; the penumbra, blind to only part of it.](https://one-course.com/images/onecourse/chapters/physics-1/g7-shadows-eclipses/fig-049b21cf6994.svg)

*A broad source’s double [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow): the [umbra](#prop-g7-shadows-eclipses-umbra), blind to the whole source; the [penumbra](#prop-g7-shadows-eclipses-umbra), blind to only part of it.*

**Example 50.3 (Soft edges everywhere).**

Now the smeared [shadows](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) of frosted lamps and cloudy skies are accounted for: broad sources wrap every [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) in [penumbra](#prop-g7-shadows-eclipses-umbra), and a big enough source (the whole overcast sky) is all [penumbra](#prop-g7-shadows-eclipses-umbra) — [shadows](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) washed to nothing. Your own noon [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s edge, looked at closely, is a soft penumbral hem a [centimetre](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) wide: the Sun is a disc, not a point, and the hem is its confession.

## 50.2 The Moon steps into the beam

**Definition 50.4 (Solar eclipse).**

A *solar eclipse* happens when the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) passes exactly between Sun and Earth, and its [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) falls on us. Where the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s *[umbra](#prop-g7-shadows-eclipses-umbra)* touches the Earth — a racing spot rarely two hundred kilometres wide — the Sun’s disc is entirely hidden: *total* eclipse, night at noon, [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) out. In the vast surrounding *[penumbra](#prop-g7-shadows-eclipses-umbra)*, the Sun is only partly bitten: *partial* eclipse.

**Definition 50.5 (Lunar eclipse).**

A *lunar eclipse* happens when the *[Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)* sails into the *Earth’s* [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) cone: the [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) darkens — often to a deep copper glow — for an hour or more, visible to the whole night half of the world at once. This time we are the blockers, and the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) stands in our [umbra](#prop-g7-shadows-eclipses-umbra).

![Solar eclipse geometry (sizes and gaps wildly not to scale): the Moon’s slender umbra just reaches the Earth — totality for the lucky spot beneath its tip.](https://one-course.com/images/onecourse/chapters/physics-1/g7-shadows-eclipses/fig-ab81d35ba8ed.svg)

*[Solar eclipse](#def-g7-shadows-eclipses-solar) geometry (sizes and gaps wildly not to scale): the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s slender [umbra](#prop-g7-shadows-eclipses-umbra) just reaches the Earth — totality for the lucky spot beneath its tip.*

**Example 50.6 (Why so rare?).**

New moon comes every month — why not a [solar eclipse](#def-g7-shadows-eclipses-solar) every month? Because the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) is *tilted*, by about five degrees, against the Earth’s path around the Sun. Most months, the new moon passes *above* or *below* the Sun–Earth line, and its [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) spears harmlessly into space. Only when a new moon happens just as the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) crosses the alignment plane do the three worlds line up — a few times a year somewhere on Earth, and for any *particular* town, totality is a once-in-lifetimes visitor.

![Totality: the Moon’s disc exactly covers the Sun’s, and for a few minutes the corona — the Sun’s outer atmosphere — hangs visible around the black disc.](https://one-course.com/images/onecourse/chapters/physics-1/g7-shadows-eclipses/img-efd9a8315581.jpg)

*Totality: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s disc exactly covers the Sun’s, and for a few minutes the corona — the Sun’s outer [atmosphere](https://one-course.com/books/physics/1/en/chapter/36-air-pressure-and-weather#def-g5-air-pressure-weather-pressure) — hangs visible around the black disc.*

**Example 50.7 (The coincidence that makes totality).**

Your sports-field model found it: the Sun is about $400$ times wider than the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) — and stands about $400$ times farther. The two discs therefore match in the sky almost exactly, so the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) can cover the Sun *just barely*: totality is brief and its umbra-spot small. When the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is at the far end of its slightly oval [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit), its disc falls short, and a burning ring of Sun rims the black [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) — an *annular* eclipse, beautiful and never safe to watch unprotected.

**Remark 50.8 (Watching without weeping).**

The old law has no eclipse exception: *never* look at the Sun — eclipsed, ringed or whole — with bare eyes, sunglasses, or any lens. A partly hidden Sun burns retinas as surely as the whole one, and painlessly. The safe instruments are old friends: the pinhole — project the Sun’s [image](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) through a small hole onto paper and watch the bite grow at comfort — or a leafy tree, whose thousand leaf-gap pinholes strew the ground with little [crescents](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes). Only certified eclipse glasses, inspected and undamaged, may face the Sun directly; during *totality’s* few minutes alone, the bare corona may be admired — and the first returning sliver ends the truce.

## 50.3 Exercises

**Exercise 50.1 ★.**

Define [umbra](#prop-g7-shadows-eclipses-umbra) and [penumbra](#prop-g7-shadows-eclipses-umbra) by what an eye inside each can see of the source.

**Solution of Exercise 50.1.**

[Umbra](#prop-g7-shadows-eclipses-umbra): the source is entirely hidden — [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) from no part of it arrives. [Penumbra](#prop-g7-shadows-eclipses-umbra): the source is partly hidden — [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) from part of it still arrives, peeking over the blocker’s edge.

**Exercise 50.2 ★.**

Why does a point-like lamp throw no [penumbra](#prop-g7-shadows-eclipses-umbra) at all? And why does an overcast sky throw almost no [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)?

**Solution of Exercise 50.2.**

A point has no “parts” to be partly hidden: every place either sees it or does not — sharp [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow), no fringe. An overcast sky is a source so broad that almost every spot sees most of it: nearly all [penumbra](#prop-g7-shadows-eclipses-umbra), [shadows](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) washed away.

**Exercise 50.3 ★.**

In the construction method, whose rays draw the [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) map — the source’s center or its edges? What marks the [umbra](#prop-g7-shadows-eclipses-umbra)?

**Solution of Exercise 50.3.**

The rays from the source’s *edges*, grazing the blocker’s sides. The [umbra](#prop-g7-shadows-eclipses-umbra) is the region both edges’ rays miss.

**Exercise 50.4 ★.**

[Solar eclipse](#def-g7-shadows-eclipses-solar): put Sun, [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) and Earth in order, and say what the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s phase must be that day. [Lunar eclipse](#def-g7-shadows-eclipses-lunar): same questions.

**Solution of Exercise 50.4.**

Solar: Sun–Moon–Earth, in that order — the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) must be new (between us and the Sun). Lunar: Sun–Earth–Moon — the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) must be full (opposite the Sun).

**Exercise 50.5 ★.**

During a [solar eclipse](#def-g7-shadows-eclipses-solar), who sees totality, who sees a partial bite, and who sees nothing unusual at all?

**Solution of Exercise 50.5.**

Totality: only those inside the [umbra](#prop-g7-shadows-eclipses-umbra)’s small racing spot. A partial bite: the great penumbral surroundings. Nothing at all: everyone the [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) regions miss — most of the [planet](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet).

**Exercise 50.6 ★.**

Why is a [lunar eclipse](#def-g7-shadows-eclipses-lunar) visible from half the world at once, while totality’s path is a narrow racing stripe?

**Solution of Exercise 50.6.**

The [lunar eclipse](#def-g7-shadows-eclipses-lunar) is the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) itself dimming — a change on an object the whole night side can see at once. Solar totality requires standing *inside* the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s slender [umbra](#prop-g7-shadows-eclipses-umbra) where it touches the ground: a spot, not a sky-wide event.

**Exercise 50.7 ★.**

Why is there no eclipse every month, despite a new moon and a [full moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) every month?

**Solution of Exercise 50.7.**

The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit) tilts about five degrees against the Earth–Sun plane: most new and [full moons](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) pass above or below the exact line, and the [shadows](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) miss. Only when phase and plane-crossing coincide do the three worlds align.

**Exercise 50.8 ★.**

List two safe ways to follow a [solar eclipse](#def-g7-shadows-eclipses-solar)’s progress, and the one moment when bare eyes are permitted.

**Solution of Exercise 50.8.**

The pinhole projection onto paper, and the leafy tree’s ground [crescents](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) (or a colander); certified, undamaged eclipse glasses for direct viewing. Bare eyes: only during totality itself, and the first returning sliver ends the permission.

**Exercise 50.9 ★★.**

Explain the $400$-and-$400$ coincidence and both of its children: the near-perfect fit of totality, and the ring of the annular eclipse.

**Solution of Exercise 50.9.**

The Sun is about $400$ times the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s width at about $400$ times its distance, so the two discs match in the sky almost exactly. Children of the fit: totality exists but only just — brief, with a tiny umbra-spot; and when the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) rides the far part of its oval [orbit](https://one-course.com/books/physics/1/en/chapter/43-the-sunearthmoon-system#def-g6-sun-earth-moon-axisorbit), its slightly smaller disc leaves the Sun’s rim uncovered — the annular ring.

**Exercise 50.10 ★★.**

Look closely at your [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s edge at noon: crisp at your feet, softer at your head’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow). Explain the gradient with the Sun’s disc and the construction method — why does [penumbra](#prop-g7-shadows-eclipses-umbra) widen with distance from the blocker?

**Solution of Exercise 50.10.**

Every [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s penumbral hem is drawn by the Sun’s edges, and the construction shows the hem widening with the gap between blocker and screen: rays from opposite solar edges spread farther apart the longer they travel past the blocker. Feet stand at zero gap — crisp; the head’s [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) lies two [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) of spreading away — soft.

**Exercise 50.11 ★★.**

During a partial [solar eclipse](#def-g7-shadows-eclipses-solar), the leafy-tree [crescents](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) of two years ago return. Explain them now in full: what is each leaf-gap, what is each ground-patch, and why do all the [crescents](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) point the same way?

**Solution of Exercise 50.11.**

Each leaf-gap is a natural pinhole camera; each ground-patch is that pinhole’s [image](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) of the Sun — round on ordinary days. During the partial eclipse the Sun itself is a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes), so every faithful little camera projects a [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) — and all point the same way because all copy the one [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) in the sky.

**Exercise 50.12 ★★★.**

During a total *lunar* eclipse the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) rarely vanishes: it glows deep copper-red. The [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) reaching it has grazed the rim of the Earth — passing through our [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) all around the [planet](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet) at once. Assemble the explanation from last chapter’s long-path [diffusion](https://one-course.com/books/physics/1/en/chapter/49-sources-of-light-and-propagation#def-g7-light-sources-propagation-diffusion): what has our [atmosphere](https://one-course.com/books/physics/1/en/chapter/36-air-pressure-and-weather#def-g5-air-pressure-weather-pressure) done to the grazing [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), and why is the survivor [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) red? (You are explaining, in one stroke, why the eclipsed [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) wears the color of every [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) on Earth.)

**Solution of Exercise 50.12.**

Sunlight grazing the Earth’s rim crosses the [atmosphere](https://one-course.com/books/physics/1/en/chapter/36-air-pressure-and-weather#def-g5-air-pressure-weather-pressure) along its longest possible roads — sunset-length paths all around the [planet](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-planet) at once. The [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) diffuses away much of the passing [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) (the share that paints Earth’s skies), and the [diffusion](https://one-course.com/books/physics/1/en/chapter/49-sources-of-light-and-propagation#def-g7-light-sources-propagation-diffusion) robs the short-path colors soonest, so the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) that survives the long grazing journey and bends on to the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) is the [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight)’s survivor: red. The eclipsed [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) glows with the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) of every [sunrise](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) and [sunset](https://one-course.com/books/physics/1/en/chapter/4-day-and-night-the-sun#def-g1-day-and-night-daynight) on Earth falling on it together.

## 50.4 Problem: The Eclipse Expedition

**Problem 50.1.**

Weekend problem — the class plans its eclipse expedition; geometry chooses the campsite, physics packs the bags; totality, minute by minute

Next spring, a total [solar eclipse](#def-g7-shadows-eclipses-solar) crosses the continent. The class plans an expedition — with ray diagrams, not brochures.

**Part I — Choosing where to stand.** The atlas shows the predicted path: a stripe $160\,\mathrm{km}$ wide running across the map, flanked by a partial-eclipse zone thousands of kilometres broad.

1. What [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) region does the stripe trace, and what region flanks it?
2. The class’s town sits $300\,\mathrm{km}$ from the stripe’s centerline. What will the town see on eclipse day?
3. Why must the expedition travel to the stripe — why will “ninety-five percent partial” at home not show night at noon, [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) , or the corona?
4. The stripe’s forecast marks totality at 10:41, lasting $3$ minutes $12$ seconds at the centerline and less toward the edges. Why is totality longest at the center of the stripe?

**Part II — Packing the physics.**

5. The teacher packs certified eclipse glasses and confiscates two pairs of sunglasses. Justify both acts.
6. Each pupil must build a pinhole projector from a shoebox. Recall its architecture, and state which way to stand relative to the Sun.
7. One pupil proposes “watching in the [reflection](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection) of a bucket of water”. Rule on the proposal.
8. The group will also carry a colander to hold over a white sheet. Predict, and explain, what its dozens of holes will paint during the partial phases.

**Part III — The day, minute by minute.**

9. 09:30, first contact: through the glasses, a small bite appears at the Sun’s edge. What body is taking the bite, and which of its [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) regions has reached the camp?
10. 10:39: the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) turns eerie and thin; [shadows](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) on the ground grow strangely sharp-edged. Explain the sharpening with umbra-and-penumbra thinking — what is the Sun becoming as its visible sliver narrows?
11. 10:41, totality: glasses off, by the rule. For $3$ minutes the class stands inside something. Name it precisely, and state what has become visible around the black disc — and why the truce ends at the first returning sliver.
12. 12:00, on the bus home, the teacher asks for the one-sentence summary: “An eclipse is…” Complete it worthily, with the chapter’s geometry inside it.

**Solution of Problem 50.1.**

**1.** The stripe is the path of the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s [umbra](#prop-g7-shadows-eclipses-umbra) racing across the ground; the broad flanking zone is the [penumbra](#prop-g7-shadows-eclipses-umbra)’s footprint. **2.** A partial eclipse: the town sits in the [penumbra](#prop-g7-shadows-eclipses-umbra) — a bite out of the Sun, watched through proper protection, and no darkness. **3.** Even a five-percent sliver of Sun is thousands of times brighter than full moonlight: it keeps the sky lit and the corona invisible. Night-at-noon belongs to the [umbra](#prop-g7-shadows-eclipses-umbra) alone — there is no “almost totality”. **4.** The umbra-spot is roughly round: a camp on the centerline sits under the spot’s full width as it races past, while camps near the stripe’s edge catch only a chord of the circle — a shorter crossing, a shorter totality. **5.** Certified eclipse glasses block the Sun’s burn; sunglasses do not — they dim glare while letting the retina-burning share through, making comfortable staring possible: worse than nothing. **6.** Pinhole in one end, tracing-paper screen at the other (or plain paper on the ground): stand with your *back* to the Sun, hole aimed over your shoulder, and watch the projected disc — never through the hole. **7.** Rejected: water’s [reflection](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection) is a [mirror-image](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) of the Sun, nearly as blinding as the Sun itself — a bounced burn is still a burn. **8.** Dozens of [crescent](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#ex-g2-moon-in-the-sky-shapes) [images](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image) on the sheet: each hole is a pinhole camera, and each projects the bitten Sun — a colander full of eclipses. **9.** The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) — invisible against the glare until its disc’s edge starts covering the Sun’s; the camp has entered the [penumbra](#prop-g7-shadows-eclipses-umbra). **10.** The visible Sun is shrinking toward a thin sliver — an ever more point-like source. Smaller source, narrower penumbral hems: every [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow)’s soft edge tightens, and the world turns strange and sharp. **11.** The [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s [umbra](#prop-g7-shadows-eclipses-umbra) itself — the class stands inside the [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) cone’s tip as it races over the camp. Around the black disc hangs the corona, the Sun’s pearly outer [atmosphere](https://one-course.com/books/physics/1/en/chapter/36-air-pressure-and-weather#def-g5-air-pressure-weather-pressure), visible only now; the first sliver of returning disc restores full daylight rules — glasses on. **12.** For example: “An eclipse is a [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) with worlds for lamp, blocker and screen: the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon)’s [umbra](#prop-g7-shadows-eclipses-umbra) brushing our ground, or the [Moon](https://one-course.com/books/physics/1/en/chapter/11-the-moon-in-the-sky#def-g2-moon-in-the-sky-moon) sailing through ours — geometry you can draw with two rays and a ruler, staged on the grandest scale in nature.”