LV: Depth of Field of + Lens Magnifiers

When we talk about depth of field we want to calculate how much the reading material can be moved before a patient notices defocus. Here's an example:

Depth of focus = 0.8D (this means 0.4D each side of the focal point)
Simple magnifier of +5.00DS is used

Method 1

the equation we use is

Δl = (1/L2 - F) - (1/L1-F)

we do one of these for each direction you can move in, and then add them together

NB L'2 = -0.4D if obj moves towards lens and +0.4D if the object moves away from the lens
so here we go

Δl = (1/5.4) - (1/-5) = 0.0148m = 15mm
Δl = (1/4.6) - (1/-5) = -0.0173m = 17mm

so total depth of field is 15 + 17 = 32mm

Method 2

Δl = -ΔL'/(4M)squared

Δl = 0.8/(4 x 1.25) squared

Remember to square both numbers of the denominator

Δl = 0.8/25 = 0.032 = 32mm

The conclusion here is that moving the object by only 16mm causes a significant amount of blur (0.4DS here) which will be perceived by the patient. Note that this example involves low magnification. The higher the magnification, the smaller the depth of field will be.