What is the equation for the total magnification of a Handheld magnifier?

• A. M = uF
• B. M = F/u
• C. M = u+F
• D. M = F−u

Answer: (A)

When you view with a relaxed eye, the amount the object appears enlarged depends on two things: how far the object is from the lens (u) and how strong the lens is (its focal power, F, in diopters, which is 1/f in meters). If the lens makes the image at infinity, the angular size of the image is about h/f, where h is the object height and f is the focal length. The unaided eye at distance u sees the object with angular size about h/u. Magnification is the ratio of these angles, so M ≈ (h/f) / (h/u) = u/f. Since F = 1/f, this becomes M ≈ uF. In other words, the total magnification is the product of how far the eye is from the object and the lens’s focal power.

For example, if the object is 0.2 m away and the lens has a focal power of 50 diopters (f = 0.02 m), the magnification is about 0.2 × 50 = 10×.

This form makes sense dimensionally (meters times diopters gives a unitless magnification) and aligns with the geometry of rays through a magnifier used with a relaxed eye.