- #1

BOAS

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- 19

## Homework Statement

A converging meniscus lens is made of glass with index of refraction n = 1.55, and its sides have radii of curvature of 4.5 cm and 9 cm. The concave surface is placed upward and filled with carbon tetrachloride which has index of refraction n' = 1.46. Using the result in (i), or otherwise, determine the focal length of the combination of glass and carbon tetrachloride.

## Homework Equations

## The Attempt at a Solution

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"The result in (i)" is that [itex]\frac{1}{f_{1}} + \frac{1}{f_{2}} = \frac{1}{f}[/itex] for two thin lenses in contact.

I think the way to approach this problem is to use the lensmakers equation to find the focal length of the converging meniscus lens, and again to find the focal length of the 'lens' formed by the carbon tetrachloride. Using the result from part (i) to combine them completes the problem.

For the meniscus lens I have [itex]\frac{1}{f} = (n-1)(\frac{1}{R_{1}} - \frac{1}{R_{2}})[/itex]

which works out the focal length to be [itex]f_{1} = 0.16[/itex]m.

My question is how to treat the second lens... Can I say that the fluid will behave like a lens with both sides having equal radius of curvature, as given by the meniscus lens it's sitting inside?

It seems to me that the fluid will have a meniscus, so saying it has a flat surface seems wrong, but at the same time, I can't think how to justify the meniscus having the same radius of curvature as that of the lens it's sitting in.

I hope that makes sense,

thanks!