A biconvex lens is formed by using two thin planoconvex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be :

Solution

Physics sir · 4 steps

Treat the biconvex lens as two planoconvex lenses in contact: add their powers, then use the lens formula.

1. Each half separately. For a planoconvex lens the flat face has R = ∞, so the lensmaker's formula reduces to 1/f = (μ - 1)/R. Left half: 0.5/15 = 1/30 cm⁻¹. Right half: 0.2/12 = 1/60 cm⁻¹.
2. Combine the halves. Thin lenses in contact add their powers: 1/f = 1/30 + 1/60 = 3/60 = 1/20, so f = +20 cm.

   1/v = 1/f + 1/u = 1/20 + 1/-30 = 1/60

3. Find the image. With u = -30 cm, this gives v = +60 cm. The image is real and forms on the other side of the lens.
4. So. For a lens m = v/u = 60/-30 = -2. The image is real, inverted and twice the size of the object, which is option (a).

The idea to keep. A lens made of two different glasses is two thin lenses in contact. Find each power from (μ - 1)/R, add them, then apply the lens formula with signs.

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