CDS (II) 2020 General Knowledge · Question 105 of 120

Correct — A, A point source and an opaque screen. Two separate conditions have to be met, and only this option meets both. The source must be a point, because every point of a source casts its own shadow of the object; with a source of finite size those shadows are displaced from one another and their overlap produces a soft grey fringe, the penumbra, around the fully dark umbra. Shrink the source to a point and there is only one shadow, so the boundary is a clean edge with no penumbra at all. The screen must be opaque, because a screen shows an image only if it stops the light that reaches it — light passing through a transparent screen is not scattered back to the eye, so there is nothing to see the pattern of light and dark on. Put the two together and a point source with an opaque screen gives the sharpest shadow.

• (b)An extended source and an opaque screen — Right screen, wrong source. An extended source such as a tube light or the Sun casts overlapping shadows from each of its points, so the shadow acquires a fuzzy penumbra and the edge is blurred rather than sharp.
• (c)A point source and a transparent screen — Right source, wrong screen. Light falling on a transparent sheet passes through instead of being stopped and scattered, so no visible pattern of light and shade forms on it — however sharp the geometry, there is no shadow to see.
• (d)An extended source and a transparent screen — Both conditions fail. The extended source blurs the edge and the transparent screen does not display the shadow at all — the worst combination of the four.

A shadow forms because light travels in straight lines and an opaque object blocks it. With a point source the shadow has only an umbra, a region receiving no light at all, and a geometrically sharp boundary. With an extended source each point of the source projects its own umbra; where those regions do not coincide the screen receives light from part of the source but not all of it, and that partially lit ring is the penumbra. The same geometry explains eclipses: an observer in the Moon's umbra sees a total solar eclipse, one in the penumbra a partial one.

The examiner has built the item as two independent yes-or-no tests stacked into one choice, so the reliable method is to run each test separately rather than judging the pairs as wholes. Test one is the source: point gives sharp, extended gives fuzzy. Test two is the screen: opaque catches the shadow, transparent lets the light through and shows nothing. Only one option passes both. Everyday experience confirms the first test — a shadow cast by a small torch bulb has a crisp edge while the same object under a broad ceiling panel has a soft one — and stage lighting and photography exploit exactly this by using small hard sources for crisp shadows and large diffused ones for soft light.

• Light travels in straight lines, which is why an opaque object casts a shadow at all.
• A point source produces only an umbra and therefore a sharp-edged shadow.
• An extended source produces an umbra surrounded by a penumbra, giving a blurred edge.
• A screen must be opaque to display a shadow; a transparent screen transmits the light instead of stopping it.
• The umbra and penumbra of the Moon's shadow are what separate a total solar eclipse from a partial one.

• Judging the option pairs as wholes instead of testing the source and the screen separately.
• Assuming a bigger or brighter source gives a sharper shadow; a bigger source gives a softer one.
• Forgetting that a screen has to be opaque to show anything at all.

As this two-condition item, as an umbra and penumbra question, or through eclipses, where the same geometry decides total against partial.

No directly related past PYQ was found.

• practice — not a real PYQ

  The completely dark central region of a shadow is called the

  • (a)penumbra
  • (b)umbra
  • (c)corona
  • (d)aperture

  Answer(b) umbra — the region that receives no light at all from the source. The partially lit ring around it is the penumbra.

• practice — not a real PYQ

  A shadow with a distinct penumbra around its dark centre indicates that the source of light is

  • (a)a point source
  • (b)an extended source
  • (c)monochromatic
  • (d)very far away

  Answer(b) an extended source — different points of a source of finite size cast slightly displaced shadows, and the region lit by only part of the source forms the penumbra.