# Focal length

For this question, assume that the index of refraction of diamond is 2.39, that of glass is 1.65, that of water is 1.30, and that of air is extremely close to 1.

A thin lens made of glass has a focal length in air of 16.1 cm. A lens of exactly the same shape is then made from diamond.

HINT: Review the derivation of the thin lens formula. Note that the index of refraction, n, used in the derivation is actually the relative index of refraction: n = n lens/n surrounding

a) What is the focal length of the diamond lens in air?

b) What is the focal length of the diamond lens in when it is immersed in water?

I was not sure at all how to even get started on this problem.

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Find out from your books or lecture notes or the web the 'lens formula' sometimes called the the 'lensmakers formula'. Then it becomes easy.

Is that (1/d o) +(1/d i)=1/f ? b/c I was looking more for a formula that related f to n.

The formula I have in mind is

1/f = (n-1)( 1/d0 + 1/d1)

which does just that.

but if I'm not given do or di, how do I go about using that equation?

You can choose any values you like that give the correct focal length for the glass lens. Easiest is to set them equal, then solve for d0.

for the value of n, is that n of the material? how would you factor in n of the outside (i.e. when the lens is immersed in water?)

Remember Snell's law that relates refractive index n to the speed of light in the material ? That will tell you how to work out the refractive index between two materials.

It's over to you now, do some research.

okay thank you so much!