1. The first lens has a front surface of +10.00DS, and a back surface of -2.00DS. The nominal power of this lens is +8.00DS, right? First we will consider it with a thickness of 20mm, then we will consider it at 5mm thick. (No, the 20mm thick one will never go in a pair of glasses. It might do in a microscope or some other imaging system; in this case it would be bi-convex. This is an exaggeration so you can see what thickness does.)
• BACK VERTEX POWER, thicker lens.

+9.54D instead of the +8.00D that we expected from the nominal power formula.
• FRONT VERTEX POWER, thicker lens.

+8.05D instead of the +8.00D that we expected from the nominal power formula.
• BACK VERTEX POWER, thinner lens.

+8.34D instead of the +8.00D that we expected from the nominal power formula.
• FRONT VERTEX POWER, thinner lens.

+8.01D instead of the +8.00D that we expected from the nominal power formula.
2. This lens has a front surface of +2.00DS, and a back surface of -10.00DS. The nominal power of this lens is -8.00DS, right? First we will consider it with a thickness of 20mm, then we will consider it at 5mm thick.
• BACK VERTEX POWER, thicker lens.

D1 = +2.00D
D2 = -10.00D
t= 20mm = 0.02m
n = 1.50 D1
DB = -------------- + D2
1 - (t/n)(D1)

+2.00
DB = ------------------------------------ + (-10.00)
1 - (0.02/1.50)(+2.00)

+2.00
DB = ------------------------ + (-10.00)
1 - (0.0266666)

+2.00
DB = ---------------------- + (-10.00)
0.97333333

DB = +2.05 + (-10.00) = -7.95DS

The back vertex power for the thick minus lens is -7.95DS instead of -8.00DS.
 
• FRONT VERTEX POWER, thicker lens.

D1 = +2.00D
D2 = -10.00D
t= 20mm = 0.02m
n = 1.50 D2
DF = -------------- + D1
1 - (t/n)(D2)

-10.00
DF = ------------------------------------- + (+2.00)
1 - (0.02/1.50)(-10.00)

-10.00
DB = --------------------------- + (+2.00)
1 - (-0.13333333)

-10.00
DB = ------------------------ + (+2.00)
1.133333333

DB = -8.82 + (+2.00) = -6.82DS

The front vertex power of the thick minus lens is -6.82DS instead of -8.00.
 
• BACK VERTEX POWER, thinner lens.

D1 = +2.00D
D2 = -10.00D
t= 5mm = 0.005m
n = 1.50 D1
DB = -------------- + D2
1 - (t/n)(D1)

+2.00
DB = ------------------------------------- + (-10.00)
1 - (0.005/1.50)(+2.00)

+2.00
DB = --------------------------- + (-10.00)
1 - (0.00666666)

+2.00
DB = ----------------------- + (-10.00)
0.993333333

DB = +2.01+ (-10.00) = -7.99DS

The back vertex power of the thin minus lens is -7.99. As close as we can get to -8.00!
 
• FRONT VERTEX POWER, thinner lens.

D1 = +2.00D
D2 = -10.00D
t= 5mm = 0.005m
n = 1.50 D2
DF = -------------- + D1
1 - (t/n)(D2)

-10.00
DF = ------------------------------------ + (+2.00)
1 - (0.005/1.50)(-10.00)

-10.00
DB = ------------------------------ + (+2.00)
1 - (-0.03333333)

-10.00
DB = ------------------------ + (+2.00)
1.033333333

DB = -9.68 + (+2.00) = -7.68DS

The thin minus lens has a front vertex power of -7.68DS instead of -8.00DS.
3. Now for the 'plano' lens. Front surface power of +6.00DS, back surface power of -6.00DS, first thickness 20mm, second thickness 5mm, always of 1.50 plastic.
• BACK VERTEX POWER, thicker lens.

D1 = +6.00D
D2 = -6.00D
t= 20mm = 0.02m
n = 1.50 D1
DB = -------------- + D2
1 - (t/n)(D1)

+6.00
DB = ----------------------------------- + (-6.00)
1 - (0.02/1.50)(+6.00)

+6.00
DB = ------------------ + (-6.00)
1 - (0.08)

+6.00
DB = ------------ + (-6.00)
0.92

DB = +6.52 + (-6.00) = +0.52DS

The back vertex power for the thick minus lens is +0.52DS instead of plano.
 
• FRONT VERTEX POWER, thicker lens.

D1 = +6.00D
D2 = -6.00D
t= 20mm = 0.02m
n = 1.50 D2
DF = -------------- + D1
1 - (t/n)(D2)

-6.00
DF = ----------------------------------- + (+6.00)
1 - (0.02/1.50)(-6.00)

-6.00
DB = -------------------- + (+6.00)
1 - (-0.08)

-6.00
DB = -------------- + (+6.00)
1.08

DB = -5.55+ (+6.00) = +0.44DS

The front vertex power of the thick minus lens is +0.44DS instead of plano.
 
• BACK VERTEX POWER, thinner lens.

D1 = +6.00D
D2 = -6.00D
t= 5mm = 0.005m
n = 1.50 D1
DB = -------------- + D2
1 - (t/n)(D1)

+6.00
DB = ------------------------------------ + (-6.00)
1 - (0.005/1.50)(+6.00)

+6.00
DB = ---------------- + (-6.00)
1 - (0.02)

+6.00
DB = -------------- + (-6.00)
0.98

DB = +6.12+ (-6.00) = +0.12DS

The back vertex power of the thinner minus lens is +0.12. Still not plano.
 
• FRONT VERTEX POWER, thinner lens.

D1 = +6.00D
D2 = -6.00D
t= 5mm = 0.005m
n = 1.50 D2
DF = -------------- + D1
1 - (t/n)(D2)

-6.00
DF = ------------------------------------ + (+6.00)
1 - (0.005/1.50)(-6.00)

-6.00
DB = ------------------- + (+6.00)
1 - (-0.02)

-6.00
DB = ----------------- + (+6.00)
1.02

DB = -5.88 + (+6.00) = -0.12DS

The thinner minus lens has a front vertex power of +0.12DS instead of plano.

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