State the surface powers required to produce the following lenses with +6.25D front curves.

a. -0.50 DS
b. +0.50 DS
c. +1.75 DS

To determine the surface powers required to produce lenses with +6.25D front curves, we need to use the lens formula:

Surface Power = Front Curve - Back Curve

The front curve is given as +6.25D for all three cases. Now let's calculate the back curves for each lens:

a. -0.50 DS:
To find the back curve, we subtract the given lens power from the front curve:
Back Curve = +6.25D - (-0.50D)
= +6.25D + 0.50D
= +6.75D

Therefore, the surface power required for -0.50 DS lens is -6.75D.

b. +0.50 DS:
Similarly, for the +0.50 DS lens:
Back Curve = +6.25D - (+0.50D)
= +6.25D - 0.50D
= +5.75D

Therefore, the surface power required for +0.50 DS lens is -5.75D.

c. +1.75 DS:
For the +1.75 DS lens:
Back Curve = +6.25D - (+1.75D)
= +6.25D - 1.75D
= +4.50D

Therefore, the surface power required for +1.75 DS lens is -4.50D.

In summary, the surface powers required for the given front curves are:
a. -0.50 DS lens: -6.75D
b. +0.50 DS lens: -5.75D
c. +1.75 DS lens: -4.50D