# Effect of gas or liquid within a compound lens system

Hi my question is if a compound lens system if filled with gas or a liquid how does it affect the system when compared to the lens system being separated by air alone. Does this affect the focal power of the system or the effective power at all.

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If the "gas or liquid" has a different refractive index than air, then yes, it will affect the system. –  RedGrittyBrick Dec 3 '12 at 22:57

The angle of refraction at the surface of a lens (or any other boundary) is given by Snell's law:

$$\frac{sin\theta_1}{sin\theta_2} = \frac{n_2}{n_1}$$

where $n_1$ and $n_2$ are the refractive indices of the two media. Suppose $n_1$ is the air and $n_2$ the glass: the refractive index of air is pretty close to one, so we have a tendancy to ignore it and just talk about a single refractive index $n$ that is the same as $n_2$.

However if you immerse your lens in water $n_1$ is very different to one, and all the angles of refraction will change and hence the focal length of the lens changes.

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One of the Gaussian equations for a compound lens system describe this : $$\phi_{\text{tot}}=\phi_1 + \phi_2 - \phi_1\phi_2\tau$$ where $\tau = \frac{t}{n}$ is the reduced distance between the lenses (or lens systems), $n$ is the index of refraction of the medium between them (the gas or liquid which you describe), and the $\phi$s are the powers where $$\phi = \frac{1}{f_e}$$ where $f_e$ is the effective focal length of each respective system or lens.

You can see from the above, for a compound system with two positive powers, the power of the combined system will increase if you increase $n$.

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