Question

The magnification of a magnifying lens of focal length 5 cm is : (final image is at $\infty$):
A) 1
B) 2
C) 3
D) 5

Answer 1

Final image of an object forms at infinity when the object is placed at focus of the magnifying (convex) lens. Now, magnification of a substance is given by the ratio of image to object distance. But for the image at infinity the magnification is measured using the approximated angular magnification formula.

Formula used:
When the image is formed at infinity i.e. the object is placed at the front focal point of the lens then using a relaxed eye the image can be viewed with a magnification of:
$MA = \dfrac{{25cm}}{f}$..................................(1)
Where,
MA is the maximum angular magnification when image is at infinity,
f is the focal length of the lens in centimeters.
Here, the constant 25 cm is an estimate of the closest distance at which a healthy naked eye can focus.

Step by step answer:
Given:

1. Focal length of the lens is $f = 5cm$.
2. Final image is formed at infinity.

To find: magnification of the magnifying lens.

Step 1
Substitute the value of f in eq.(1) to get the magnification value as:
$MA = \dfrac{{25cm}}{{5cm}} \\\ \therefore MA = 5 \\\$

Correct answer:The magnification of the magnifying glass is (d) 5.

Note: Many students might get confused while trying to find the magnification of the lens using the ratio of image to object distance formula. Since, the image is at infinity they’ll get the magnification infinity, but practically that’s not possible. Always remember that, the ratio of object to image distance is only valid when the formed image is at some finite distance. Otherwise, you need to use the approximated angular magnification formula as given in eq.(1).