Question

A lens of power +2 diopter is placed in contact with a lens of power -1 diopter. The combination will behave like
A.) a converging lens of focal length 50 cm
B.) a divergent lens of focal length 100 cm
C.) a converging lens of focal length 100 cm
D.) a converging lens of focal length 200 cm

Answer 1

There are basically two types of lens, one is a converging lens which is also known as convex lens and the other one is a diverging lens which is also known as Concave lens. The converging lens converges the light rays to one point and forms a real image while the diverging lens diverges the light away from the principal axis and forms a virtual image behind the lens.

Complete step-by-step solution:
In this question, we are given two lenses, one lens has a power of +2 Diopter and the other lens has a power of -1 Diopter.
${{P}_{1}}=+2\text{ }Diopter$
${{P}_{2}}=-1\text{ Diopter}$
When we have power given for different lens, the net power or the power of combination can be given by
$P={{P}_{1}}+{{P}_{2}}$
Putting the values, we get
$P=(+2)+(-1)$
$P=+1\text{ Diopter}$
We also know that
$P=\dfrac{1}{F}$
Where “F” is the focal length in meters
Or we can also write,
$F=\dfrac{1}{P}$
Putting the values, we get
$F=\dfrac{1}{1}$
F = 1 Meters
Or we can say, F = 100 cm
Since, the focal length is positive, we can say that it will behave as a converging lens or as a convex lens of power +1 Diopter and focal length 100 cm
Therefore, Option (c) is the correct answer.

Note: A Converging lens has a positive focal length as the image is formed on the right side of the lens and the image formed is real and inverted. While in case of diverging lens, since the light rays do not actually meet at one point and hence, the image formed is virtual and on the left side of the lens. Therefore, a diverging lens has a negative focal length.