## Tuesday, January 27, 2015

### Power and Focal Length of a Lens

Power of a lens

It is the measure of ability to produce a convergence or divergence of parallel light rays of light. It is mathematically the reciprocal of focal length of a lens. We can express the power of a lens in terms of meters as well as centimeters as shown below.

If a portion of the light that is striking the lens is obstructed, the image formed by the lens will have less intensity but of same focal length.

If a lens is immersed in a medium whose refractive index is less than that of the material of the lens, the nature of the lens remains the same.

If a lens is immersed in a medium whose refractive index is more than the refractive index of the material of the lens, the nature of the lens will be reversed. It means a convex lens in this case behaves like a concave lens and vice versa.

If a lens is immersed in a medium whose refractive index is equal to the refractive index of material of the lens, the lens behaves like a plain glass and its focal length will become infinite.

When a lens is cut parallel to its principal axis, its focal length refractive index and radius of curvature remains the same. But the intensity of the image formed is reduced.
When a lens is cut perpendicular to the principal axis, it’s curved nature decreases and hence focal length increases. But the intensity of the image will be the same.

We can write the formula for the effective focal length and the effective power of a lens as shown below.

Problem and solution

A air lens with equal radius of curvature of 10 cm is cut in the glass cylinder as shown. Determine the focal length and the nature of the air lens. If the liquid of refractive index 2 is filled in the lens, what will happen to the focal length of the lens and how does the nature of the lens will change?

We can find the focal length of the lens using the lens makers formula. Basing an answer, we can confirm that the air lens behaves like diverging lens. When the air bubble is filled with the liquid of refractive index 2, the nature of the lens will be reversed and it behaves like a converging lens of the same focal length. The detailed solution is given below.

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