Question

An object is placed at a distance of 60 cm from a concave lens of a focal length of 30 cm.

(i) Use the lens formula to find the distance of the image from the lens.

(ii) List four characteristics of the image (nature, position, size, erect/inverted) formed by the lens in this case.

(iii) Draw a ray diagram to justify your answer to the part

Answer 1

(i) Find the distance of the image from the lens

Step 1: Given:

Object distance, u = − 60 cm

Focal length of the lens, f = −30 cm

Step 2: Finding the image distance using the lens formula:

Using the lens formula, we get

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u}(where\mathit{f}isthefocallength,\mathbf{}\mathit{v}istheimagedistance,and\mathit{u}istheobjectdistance) \\ Itcanberearrangedas\frac{1}{v}=\frac{1}{f}+\frac{1}{u} \\ Substitutingthegivenvaluesweget \\ \frac{1}{v}=\frac{1}{-30}+\frac{1}{-60} \\ \frac{1}{v}=\frac{1}{-30}-\frac{1}{60} \\ \frac{1}{v}=\frac{-2-1}{60} \\ \frac{1}{v}=\frac{-3}{60} \\ \frac{1}{v}=\frac{-1}{20} \\ v=-20cm \end{gathered}$$

Thus, the distance of the image from the lens is 20cm.

(ii) The four characteristics of the image (nature, position, size, erect/inverted) formed by the lens in this case are:

1. The image formed is virtual as the given lens is a concave lens.
2. The image is erect as it is formed above the principal axis.
3. Image is diminished (smaller than the object).
4. Image is formed at a distance of 20 cm from the optical center of the concave lens on the same side of the object.

(iii) The ray diagram to justify the answer to the part (ii) is given below: