Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is __________ cm.

Solution

Physics sir · 3 steps

The liquid between two convex lenses forms a third lens, a concave one. Add all three powers.

1. Radius of each lens. For a biconvex glass lens with equal radii, the lens maker's formula gives 1/15 = (1.5 - 1)2/R. So R = 15 cm.
2. The liquid lens. The liquid fills the gap between two outward-bulging surfaces. It takes the shape of a biconcave lens with both radii equal to 15 cm. Its focal length is 1/fₗ = (1.25 - 1)(-2/15) = -1/30, so fₗ = -30 cm.

   1/F = 1/15 + 1/15 - 1/30 = (2 + 2 - 1)/30 = 1/10

3. So. The three thin lenses are in contact, so their powers add. The combination has a focal length of 10 cm.

The common slip: 7.5. Leaving out the liquid lens and combining only the two glass lenses gives 1/F = 2/15, which is 7.5 cm, not 10.

The idea to keep. Whenever a liquid fills the gap between lenses, treat it as a lens of its own. Find its shape from the surfaces around it, then add the powers of all the lenses.

Answer from the NTA final answer key. Solution by PrepWiser.