What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens

What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

Focal length of the convex lens, f1 = 30 cm

Focal length of the concave lens, f2 = −20 cm

Focal length of the system of lenses = f

The equivalent focal length of a system of two lenses in contact is given as:

`1/"f" = 1/"f"_1 + 1/"f"_2`

`1/"f" = 1/30 - 1/20`

= `(2 - 3)/60`

= `-1/60`

∴ f = −60 cm

Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens.

  Is there an error in this question or solution?

What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.

Answer:

According to the question –

Focal length of the convex lens is f1=30cm

Focal length of the concave lens is f2= -20cm

Focal length of the system of lenses is denoted  by f

The equivalent focal length of the given system of lenses is given as:

$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

$\frac{1}{f}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$

Therefore f=-60cm

As a result, the focal length of the lens combination is 60cm. In addition, the negative sign indicates that the lens system in use is a diverging lens.