In the following figure, the space b/w the glass lenses is filled with

[zorro]

In the following figure, the space b/w the glass lenses is filled with water. We have to find the focal length of the system (radii of curvature, refractive indices given)

[URL]http://203.196.176.41/VLEBT_RootRepository/Resources/6c32207c-7c5a-4462-b90c-89b0c196bc72.gif[/URL]

Now to calculate the focal length of the system of lenses, we have to calculate the focal length of each lens. To find the same for water lens, we use lens maker's formula-
1/f = (μ-1)(1/R1 - 1/R2)
Why don't we substitute μ as _gμ_w instead of _aμ_w as given in all books? Doesn't the light travel from glass to water?

 

[santo35]

if i understood your question rite, it is 100 % correct to use refractive index of glass wrt water in this sum...

 

[zorro]

can you show me a source for that claim?

 

[aim1732]

Use the basic formula for refraction at a curved single interface twice,factoring in the assumption of thin lenses.You will see that terms cancel out and the final equation will agree with what you are saying.The 1 in the lens maker's formula you brandished is because the refractive index of air is very close to 1.If I remember correctly the basic equation of which the lensmaker's formula is a special case is:

n₁/u + n₃/v = n₂-n₁/R₁ + n₃-n₂/R₂
Where n₁,n₂,n₃ are refractive indices of medium to the left,the lens and the medium to the right respectively.

 

[sardar]

I would like to clarify that the value of μ (refractive index) should not be substituted as gμw (refractive index of glass) for the water lens. This is because the light does not travel from glass to water in this system. The light instead travels from air to glass, then from glass to water, and finally from water to air. Therefore, the correct value to use for μ in the lens maker's formula is aμw (refractive index of air). This is a common mistake and it is important for accurate calculations to use the correct values in the formula.