Question

1. Define $1dioptre$ of power of a lens.
2. A convex lens forms a real and inverted image of a needle at a distance of \[50cm\] from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.
3. Find the power of a concave lens of focal length $2m$.

Answer 1

Hint:To solve these questions, first we need to define the power of a lens with respect to its relation with the focal length of the lens. Then for the second question, we will find the position for real and equal size images and then by finding the focal length, we will find the power of the lens. Finally, in the last question as the focal length is given, we will find its power according to definition of the power.

Complete step by step answer:
Answer 1. We know that the function of a lens is to converge the rays falling on it. This ability of a lens is known as the power of a lens. $1dioptre$ is defined as the power of the lens having the focal length of \[1m\]. The power of the lens is given by the formula:
$P = \dfrac{1}{f}$
where $P$ is the power of the lens and $f$ is the focal length of the lens.

Answer 2. Here, we are asked the position of the needle for the image to be of inverted and equal size. We know that in the case of a convex lens the image will be equal size and inverted if the object is placed at the centre of the curvature of the lens which is $2f$. The position of the image is also at the same point. Therefore we can say that,
$2f = 50 \\
\Rightarrow f = 25cm \\
\Rightarrow f = 0.25m \\
\Rightarrow f = \dfrac{{25}}{{100}}m$
Now, we will use the formula $P = \dfrac{1}{f}$.
$ \Rightarrow P = \dfrac{{100}}{{25}} \\
\therefore P= + 4D$

Answer 3. We are given that the focal length of the concave lens is $2m$. Therefore we will take $f = - 2m$.
$P = \dfrac{1}{f} \\
\Rightarrow P = \dfrac{1}{{ - 2}} \\
\therefore P = - 0.5D$

Note:Here, we have seen that the power of convex lens is positive and that of concave lens is negative. This difference can be used in their application for glasses. For example, convex lenses are used for the farsighted and concave lenses are used for the nearsighted.