Lensmaker's formula question ( studying for abo-ac )

[Alteaon]

I am studying for the abo-ac, and have been going through the Optical Formulas Tutorial ( E. Stoner ). I am working on the lens maker's formula section and notice that the I get an opposite sign on the final answer than the answer has.
If the front side is convex ( plus power ) and the back side is concave ( minus ) and there is more power on the concave side, shouldn't the end result be minus?

Problem: ( section three, #26 )

Lens is n= 1.60, convex surface w/ radius of 8 cm and a concave side w/ radius of 15 cm. What is the power:

Calculation: 1.60-1/.08 meters= +0.75; 1.60-1/.15 meters)= -4.00; -4.00+0.75=-3.25.

Book gives answer as +3.50.

I'm pulling my hair out trying to figure this one out. Any help would be appreciated.

[Uncle Fester]

Draw 2 lines 16 and 30 cm respectively (or cut the size in half for convenience of scale). Put compasses at their midway point and draw a semi circle from one end to the other.

Which is steeper?

[Alteaon]

I don't have a compass near me. I would say that, in your example that 16 would be steeper. that means that in my problem, the concave side ( 15 cm ) would be flatter. If I'm understanding correctly, this would determine the resulting power to be plus, even though the formula shows more minus than plus? I'm sure the concept is simple but math is tough for me to visualize. I appreciate your patience and your reply

[optical24/7]

Run your convex calc again......( your answer has a decimal misplaced)

[Robert Martellaro]

Hint: For the front curve, input .08M instead of .8M for the denominator. I made a similar mistake recently- the longer I looked at it, the less obvious my error became.

[Uncle Fester]

I don't have a compass near me. I would say that, in your example that 16 would be steeper. that means that in my problem, the concave side ( 15 cm ) would be flatter. If I'm understanding correctly, this would determine the resulting power to be plus, even though the formula shows more minus than plus? I'm sure the concept is simple but math is tough for me to visualize. I appreciate your patience and your reply

edit- Upon further reading this may be redundant to the poster but I'll leave it up for anyone still confused.

Picture a dime cut in half = 8cm Now picture a quarter cut in half = 15cm Which curve is steeper? The dime represents the convex the quarter the concave. Can you visualized the dime semi circle being the + (steeper front) surface of the lens while the quarter is the - (flatter back) surface...so it has to be a net plus power?

"See it"???

[If this is coming from overseas use a smaller coin and a coin twice as big to make or "see" the different curves.]

[MakeOptics]

I am studying for the abo-ac, and have been going through the Optical Formulas Tutorial ( E. Stoner ). I am working on the lens maker's formula section and notice that the I get an opposite sign on the final answer than the answer has.
If the front side is convex ( plus power ) and the back side is concave ( minus ) and there is more power on the concave side, shouldn't the end result be minus?

Problem: ( section three, #26 )

Lens is n= 1.60, convex surface w/ radius of 8 cm and a concave side w/ radius of 15 cm. What is the power:

Calculation: 1.60-1/.08 meters= +0.75; 1.60-1/.15 meters)= -4.00; -4.00+0.75=-3.25.

Book gives answer as +3.50.

I'm pulling my hair out trying to figure this one out. Any help would be appreciated.

Front = (1.60 -1)/0.08 = 7.50
Back = (1 - 1.60)/0.15 = -4.00

Lens Maker's Equation = L1 + L2 = Power

Power = 7.50 + (-4.00) = 3.50

If you look at the back surface equation I have the index of air and material reversed from the front. We are traveling with the ray so the front goes from air (1) to mid-index (1.60), the back surface interface goes from the material (1.60) to air (1). This way the sign of the power comes out correct and the equation is more self explanatory (less verbose).

[Craig]

Front = (1.60 -1)/0.08 = 7.50
Back = (1 - 1.60)/0.15 = -4.00

Lens Maker's Equation = L1 + L2 = Power

Power = 7.50 + (-4.00) = 3.50

If you look at the back surface equation I have the index of air and material reversed from the front. We are traveling with the ray so the front goes from air (1) to mid-index (1.60), the back surface interface goes from the material (1.60) to air (1). This way the sign of the power comes out correct and the equation is more self explanatory (less verbose).

Are you sure you are qualified to answer such a technical question? I was lost half-way and figured what you said sounds good to me so it msut be correct.

Get ready to design your own lenses in the future.
Craig