How do I calculate dioptric power of lens given
1) index of lens is 1.58 polycarbonate
2) Lens is for swimming goggles so front surface is submerged in water and back surface is air (assume index of water is 4/3)
3) lens clock, the device used to measure front and back power is only calibrated to accurately measure crown glass (index 1.523)

Front curve is reading +2.00D
Back curve is reading -4.00D

Question

How do I calculate dioptric power of lens given 
1) index of lens is 1.58 polycarbonate
2) Lens is for swimming goggles so front surface is submerged in water and back surface is air (assume index of water is 4/3)
3) lens clock, the device used to measure front and back power is only calibrated to accurately measure crown glass (index 1.523)

Front curve is reading +2.00D 
Back curve is reading -4.00D

anonymous · Answer

Is there no other information given? I just took a pretty intense optics course and I am pretty sure there is not enough information given to calculate a dioptric power.

Dioptric power is related to focal length inversely. To find a focal length requires the indices of refraction, but also radii of curvature. I'm remembering the equation:
$$\frac{1}{f}=\frac{n_{l}-n_{m}}{n_{m}}(\frac{1}{R_{1}}-\frac{1}{R_{2}})$$

anonymous · Answer

edited question:  
Front surface power as read by lens clock +2.00D
Back surface power as read by lens clock -4.00

True power of front curve compensating for difference in calibration between lens clock and material being measured:

$$R=(n-1)/D$$

R is radius of curvature
n is refractive index
D is dioptric value displayed on measuring device

$$R=(1.523-1)/2$$
$$R=0.2615$$

$$D = (n-1)/R$$
$$D = (1.58-1)/0.2615$$
$$D = 2.22$$

So the thing is, this is all in air... I don't know how to use this equation and find the front surface power in water....?

anonymous · Answer

Ahh okay, so you had some powers given. That makes more sense.

Yeah, I would think for the water scenario, you just need to replace the 1 in your equation. That 1 is in there I believe to represent the index of refraction of air. You'd just have to substitute in water instead.

anonymous · Answer

Can I calculate by doing the following?
$$D = (1.58-1.33)/0.2615$$ 

I tried subbing in 1.33 in lieu of 1 while calculating both Radius of curvature and Dioptric power

I'm just not sure if I should use 1.33 for both equations or just for calculating D?

anonymous · Answer

I've never done this specifically, but assuming that the 1 in the equation is for air, I would imagine you need to substitute for water any time you perform a calculation. So it should be appropriate to do it for both.