Question

two thin convex lenses as made of glass are placed in close contact with each other .the focal length of each lens is f. If the space between the two lenses is filled with same glass material as shown ,then the effective focal length of the system is :
f
2f
3f
3/2f ​

Answer 1

The effective focal length of the system is f

Explanation:

If the focal length of two convex lenses is $f_1$ and $f_2$ and they are in close contact with each other

Then the effective focal length of the system is given by

$\fra{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

However if third material is added in between such that the it acts as concave lens with focal length $f_3$

Then, the effective focal length is given by

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{1}{f_3}$

Here, given that

Two lenses that are in close contact have focal length $f$

And, the space between them is filled by same glass material

Since the refractive index is same and the radius of curvature of the lens is also same

Therefore, this diverging lens will also have focal length $f$

Therefore,

The effective focal length

$\frac{1}{F}=\frac{1}{f}+\frac{1}{f}-\frac{1}{f}$

$\implies \frac{1}{F}=\frac{1}{f}$

$\implies F=f$

Therefore, the effective focal length of the system is f

Hope this answer is helpful.

Know More:

Q: An optical system uses two thin convex lenses in contact having the effective focal length of 30/4cm If one lens has focal length of 30cm. find the focal length of the other lens.

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