Light - Part XI

Case 5 : Image formed by a convex lens when the object is placed at a distance beyond 2 F₁.

Consider the following figure.

Let the object be a candle AB placed at a distance beyond 2 F₁.  

Applying similar treatments for the rays of light emanating from two extremes of the candle AB. A ray of light AD parallel to XY will be deflected along DF₂A’ (rule1). Another ray of light AO will be refracted along AOA’ (rule 2). Where the two rays DF₂A’and AOA’ meet, we get the image of A as A’. As explained earlier, light from B will go un-deflected along XY path. The image of AB is A’B’. Clearly the image is reduced and inverted. The image is formed between F₂ and 2 F₂.

Thus we can conclude that for an image of an object placed at a distance beyond the 2 F₁ of a convex lens:

• The image is formed between F₂ and 2 F₂

• The image is inverted and real

• The image is reduced in size.

The above geometry is used in a simple camera lens, where the picture is reduced in size and is taken on a photographic film.  

Case 6 : Image formed by a convex lens when the object is placed at a distance far off (or infinite distance) beyond 2 F₁.

Consider the following figure.

Let the object be a candle AB placed at infinity.  B is still on line XY. Rays emanating from A are striking the mirror in parallel fashion. They will be refracted and they will meet at the focal point F₂ 
(rule 3). The image is thus highly diminished.

Thus we can conclude that for an image of an object placed at an infinite distance beyond 2 F₁ of a convex lens :

• The image is formed at F₂

• The image is inverted and real

• The image is highly reduced in size

The geometry used in case 6 is what happens in a telescope that collects light from objects such as stars placed at infinity.

Uses of convex lenses  
From the cases studied above, we can now understand why convex lenses are widely used to capture or project images.

• Case 1 shows why convex lenses are used as magnifying glasses or in microscopes.

• Case 3 shows why convex lenses are used in a slide film projector.

• Case 5 shows why convex lenses are used in cameras.

• Case 6 shows why convex lenses are used in telescopes.
  

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