In this experiment, you will investigate how the size of a shadow depends on the distance between an opaque object and a point source of light. You places a...

(a) As the distance d between the lamp and the disc increases, the shadow diameter decreases. [1]

Moving the disc further from the lamp (and closer to the screen) reduces the geometric magnification. The diverging light rays from the point source subtend a smaller angle relative to the disc when it is further away, producing a smaller shadow.

(b) From Table 5.1, the shadow diameter when d = 50 cm is 10.0 cm. [1]

Magnification:

\[ m = \frac{\text{shadow diameter}}{\text{disc diameter}} = \frac{10.0}{5.0} = 2.0 \] [1]

This can be verified using similar triangles. When d = 50 cm, the disc-to-screen distance is \( 100 - 50 = 50 \) cm. By similar triangles, the magnification is \( \frac{\text{lamp-to-screen distance}}{\text{lamp-to-disc distance}} = \frac{100}{50} = 2.0 \), which agrees.

(c) With an extended (large) light source, the shadow would have a fuzzy edge, with a region of partial shadow (penumbra) surrounding a darker central shadow (umbra). [1] This occurs because light from different parts of the extended source reaches different parts of the shadow region. Some areas behind the disc receive light from part of the source but not all of it, creating a gradual transition from full shadow to full illumination. [1]

(d) The distance between the lamp and the screen should be kept constant (at 100 cm). [1] The disc diameter must also remain the same. Changing either variable would alter the shadow size independently of d.

(e) The edge of the shadow may not be perfectly sharp, making it difficult to judge exactly where to measure the diameter. [1] Even with a small lamp, the filament has a finite size, so there is always a slight penumbra that blurs the boundary.