Two lenses, one with a focal length f₁ = +20 cm and the other with a focal length f₂ = -20 cm, are on the same axis and 60 cm apart as shown. A real object is 40 cm to the left of the positive lens. The image formed by the negative lens is A) real and 10 cm from the negative lens. B) virtual and 10 cm from the negative lens. C) at infinity. D) virtual and 20 cm from the negative lens. E) None of these is correct.

Question

Quizplus · Accepted Answer

The positive lens will form a real image of the object at a distance of 60-20-20=20 cm to its right. This real image will serve as the object for the negative lens.

Using the lens equation for a negative lens:

1/f = 1/dO + 1/dI

where f is the focal length of the negative lens, dO is the object distance from the negative lens, and dI is the image distance from the negative lens.

Since the negative lens is forming a virtual image, dI will be negative. Also, since the object is to the left of the negative lens, dO will be negative. Therefore:

1/-20 = 1/-20 + 1/dI
-1/20 = 1/dI
dI = -20 cm

So the virtual image formed by the negative lens is 20 cm to its left, which is 10 cm to the right of the real image formed by the positive lens. This virtual image is also 10 cm to the left of the negative lens, so the correct answer is B.

Two Lenses, One with a Focal Length F1 = +20

Two Lenses, One with a Focal Length F₁ = +20