Question

An equiconvex lens has surfaces of radius of curvature 40 cm each. It is made of two parts as shown in Fig. An object is kept at a distance of 80 cm from the lens. Which of the following statements is correct?

(1) There is one image at a distance of 80 cm only.

(2) There is one image at a distance of 133.3 cm only.

(3) There is one image at a distance of 80 cm and another image that 20 cm away from the first image.

(4) There are two images that are 53.3 cm away from each other.

Answer 1

(4) There are two images that are 53.3 cm away from each other.

Let f₁ and f₂ respectively be the focal length of the two parts of lens, made from material of μ₁ = 1.5 and μ₂ = 1.4. Then from Lens Maker’s formula,

For both the parts of lens, of focal length f₁ and f₂ , u = –80 cm. Le v₁ and v₂ be the position of the image due to two parts of the lenser. Then

The distance between the two images = (133.3 - 80) cm = 53.3 cm