Because a concave lens cannot form a real image of a real object, it is difficult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the...

Because a concave lens cannot form a real image of a real object, it is difficult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the concave lens. Under the proper conditions, the concave lens will form a real image of the virtual object!

A student conducting a laboratory project on concave lenses makes the following observations: when a lamp is placed 42.0 cm to the left of a particular convex lens, a real (inverted) image is formed 37.5 cm to the right of the lens. The lamp and the convex lens are kept in place while a concave lens is mounted 15.0 cm to the right of the convex lens. A real image of the lamp is now formed 35.0 cm to the right of the concave lens. What is the focal length of each lens?

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

We need a formula which establishes a relation between a lens' focal length `F,` a distance `d` from an object to the lens and a distance `f` from an image to a lens.

For a convex (collecting) lens and a real image the formula is

`F=(d*f)/(d+f),`

for a concave (diverging) lens and a virtual image the formula is

`F=(d*f)/(d-f).`

 

Please look at the picture attached. The focal length of the convex lens is

`F_(convex)=(42*37.5)/(42+37.5) approx 19.8 (cm).`

For the concave lens the object is the real image produced by the convex lens. So the distance between the lens and the object is 37.5-15=22.5(cm). The distance from the concave lens to its real image is given (35 cm). Therefore its focal length is

`F_(concave)=(22.5*35)/(22.5-35) approx -63(cm).`

Yes, it is negative because the lens is diverging.

The answer: the focal length for the convex lens is 19.8 cm and for the concave lens is 63 cm (or -63 cm).

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