# 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?

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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).