# Double Concave Lenses

## Concave lenses refract parallel light waves, causing them to disperse.

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Images in Double Convex Lenses and Double Concave Lenses

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At least one of the faces of a lens is part of a sphere:

• convex lenses, or converging lenses, are thicker at the center than at the edges – they bulge outwards
• concave lenses, or diverging lenses, are thicker at the edges than at the center – the faces cave inwards

Remember: the mirror equation and the magnification equation apply to lenses, too – the mirror equation is just called the lens equation now! With concave lenses, though, the focal length has to be negative.

#### Double Convex Lenses

[Figure1]

As with mirrors, you trace a parallel ray and a ray through the focus from the object. Why do lenses refract the rays?

Note: 2F refers to the point that is double the focal length away from the lens.

In the following sketch, is the red or green arrow the object? What type of image does this set-up create?

[Figure2]

Fill out the following table to sort out the characteristics of images of double convex lenses with different object distances:

 Object placement (do) Real or virtual? Upright or inverted? Enlarged or diminished? Image distance (di) Outside 2F real inverted diminished between F and 2F Between 2F and F real inverted enlarged beyond 2F inside F virtual upright enlarged negative

#### Double Concave Lenses

All rays diverge after passing through a concave lens. If parallel rays approach a concave lens, where do they refract? Can double concave lenses create real images?