Quick Question re: surface area?

[ballaratdragons (Ken)]

Just a quick question for anyone.
I can't work out the Math to get the answer.

How much extra surface area on a 10" mirror compared to an 8" mirror?

[silvinator]

Hello Ken. I'm getting a weird figure trying to work this out myself. I'm using the formula for the area of a circle and get 25pi for the 10" and 16pi for the 8". Now when I plug this in to see what the percentage increase is, I get a 1.5625 which translates to a 56.25% increase in surface area from 8" to 10". That sounds like too much to me But you just can't dispute the maths...unless I did the maths wrong

[ballaratdragons (Ken)]

Tough one isn't it!

Yes Silvie, 56.25% sounds a bit wierd.

[Mombat]

i got the same results as you silvie dunno try drawing them out see the difference visually

[ballaratdragons (Ken)]

56.25% might be right as I know that a 12" mirror is 9 times!! the area of a 4".

[silvinator]

Well, let's think of it this way (all calculations are based on cm2 for the unit of area). The area of an 8" mirror is roughly 324 cm2 and that of a 10" mirror is roughly 507 cm2. The difference in area is then 507 cm2 - 324 cm2 = 183 cm2. Now if you compare that value to the surface area of the 8", 183 cm2 ends up being about 56% the size of that area, so a 56.25% increase in surface area from 8" to 10" doesn't sound so weird after all.
Or perhaps I've just confused everyone (and even myself!) just a little more!

[Mombat]

Yeh sounds right and it would be pretty wierd if we managed to both get it wrong and get the same values. I remember being suprised at the increase in surface area from a 12" to a 14" so why would it be any different from an 8 to a 10.

[ballaratdragons (Ken)]

Thanks Silvie, Aragorn and Mombat.

Tough stuff all this area of circle comparisons.

[Starkler (Geoff)]

increase in area = (10/8)^2 = 1.5625

[ballaratdragons (Ken)]

Starkler,

Sorry but 1.5625 what?

Percent? inches? huh?

[Starkler (Geoff)]

The 10 incher has 1.5625 times the surface area of the 8 inch and therefore collects extra light in that proportion.

[ballaratdragons (Ken)]

WOW! It just doesn't seem right does it.

Thanks Starkler, I may have to go up to 10" as that is an impressive increase.

[Striker (Tony)]

I am pretty good with maths and approx 50% increase sounds about right to me....

[Starkler (Geoff)]

Actually the human eyes response to light is logarithmic rather than linear, so it doesnt mean you will perceive everything to be 1.5 times as bright.

The difference going from 8 inch to 10 inch is subtle rather than striking. Similarly with going from 10inch to 12.

If you are looking for a worthwhile increase you might want to skip a size. ie go from 6 to 10 inch, or 8 inch to 12.