Why is shadow of an object larger than the object when light is close

Question

Why is the shadow of an object larger than the object itself when the light source is placed very close to it? What happens to the shadow size as you move the light source farther away?

Solution — Step by Step

A shadow forms when an opaque object blocks light from reaching a surface (screen). Light travels in straight lines, so the blocked region on the screen is the shadow. The size of the shadow depends on how the light rays diverge around the object.

When a point source of light is very close to an object, the light rays strike the object at steep angles from many directions. The rays that just graze the edges of the object are highly divergent — they spread outward at large angles.

Imagine the light as a fan of rays spreading from a point. The object intercepts some rays, and those rays would have continued to hit a large area of the screen. Blocking those widely-spread rays creates a large shadow.

Let’s set up the geometry. Let:

$d$ = distance from light source to object
$D$ = distance from light source to screen
$h$ = height of the object
$H$ = height of the shadow

By similar triangles (rays from the point source):

\frac{H}{h} = \frac{D}{d}

So shadow size $H = h \times \frac{D}{d}$ .

When the light is close (small $d$ ), the ratio $D/d$ is large → large shadow.

As the light source moves farther from the object (larger $d$ ), the ratio $D/d$ decreases. The shadow shrinks.

At a very large distance, $D/d \approx 1$ (if screen distance is comparable to source distance) and the shadow is nearly the same size as the object.

At infinity (parallel rays, like sunlight), the shadow is exactly the same size as the object.

Why This Works

The key insight is that a close light source creates diverging rays — the rays spreading from a nearby point hit the object from many angles. The shadow is effectively a magnified projection of the object. This is exactly the same principle used in a projector: the bulb is close to the film/slide, creating a large projected image on the screen.

The formula $H/h = D/d$ is derived from the geometry of similar triangles — no complex physics, just straight-line propagation.

This same principle explains why shadows are smaller (and more defined) in bright sunlight — the Sun is so far away that its rays are nearly parallel. Near a table lamp, shadows are large and blurry.

Alternative Method

Think of it from the perspective of the object blocking rays. A close source sends rays in a wide cone. The object blocks rays that would have spread across a large area of the screen. A far source sends nearly parallel rays — the object blocks only a narrow column of rays, forming a shadow its own size.

Common Mistake

Students often think “the light is stronger close up, so the shadow is larger.” Light intensity has nothing to do with shadow size. Shadow size depends purely on geometry — the angle at which rays diverge around the object. Two identical lights at different distances will produce different shadow sizes regardless of their brightness.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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