Question

A student uses a converging lens to produce an enlarged virtual image of a scale she wishes to read accurately. The focal length of the lens is \[10\,{\text{cm}}\]. What is a suitable distance between the scale and the lens?
A. \[8\,{\text{cm}}\]
B. \[10\,{\text{cm}}\]
C. \[15\,{\text{cm}}\]
D. \[20\,{\text{cm}}\]

Answer 1

Hint:We have given that the students want to obtain a virtual and enlarged image of the scale so that she can read the scale accurately. Recall the formation of the image using a converging lens. Hence, explain what should be the position of the scale so that the student can read the readings on the scale accurately.

Complete answer:
We have given that the student wishes to have an enlarged virtual image of the scale using a converging lens in order to read the scale accurately. The focal length of the converging lens used by the student is \[10\,{\text{cm}}\].
\[f = 10\,{\text{cm}}\]
We know that we can obtain an enlarged virtual image of an object with the help of a converging lens only when the object is placed between the lens and focal point of the lens.

Here, we have given that the focal point of the converging lens used by the students is at a distance \[10\,{\text{cm}}\] from the converging lens. Thus, to obtain an enlarged virtual image of the scale, the students should place the scale at a distance less than \[10\,{\text{cm}}\] from the lens.In the given options, there is only one option which has distance less than \[10\,{\text{cm}}\] which is \[8\,{\text{cm}}\] given in option A.Therefore, the suitable distance between the lens and scale to read the scale accurately in the image of the scale is \[8\,{\text{cm}}\].

Hence, the correct option is A.

Note: One can also solve the same question by another method. One can use the lens formula to solve the question. The focal length of the converging lens is given in the question. The image distance can be taken 25 cm as it is the least distance of distinct vision. Then using lens formula one can calculate the distance of scale from the lens (object lens) for enlarged and virtual image. Round off the distance of the object from the lens obtained to the nearest value given in the option.