Question

Figure 5.9 illustrates an aligned system consisting of three thin lenses. The system is located in air. Determine:

(a) the position of the point of convergence of a parallel ray incoming from the left after passing through the system; 

(b) the distance between the first lens and a point lying on the axis to the left of the system, at which that point and its image are located symmetrically with respect to the lens system.

Answer 1

(a) Path of a ray, as it passes through the lens system is as shown below. Focal length of all the three lenses,

f = 1/10 m = 10 m,  neglecting their signs. 

Applying lens formula for the first lens, considering a ray coming from infinity,

and so the position of the image is 5 cm to the right of the second lens, when only the first one is present, but the ray again gets refracted while passing through the second, so

or, s' = 10 cm, which is now 5 cm left to the third lens so for this lens,

(b) This means that if the object is x cm to be left of the first lens on the axis OO' then the image is x on to the right of the 3rd (last) lens. Call the lenses 1,2,3 from the left and let to be the object, O₁ its image by the first lens, O₂ the image of O₁ by the 2nd lens and O₃ , the image of O₂ by the third lens. 

O₁ and O₂ must be symmetrically located with respect to the lens L₂ and since this lens is concave, O₁ must be at a distance 2| f₂ | to be the right of L₂ and O₂ must be 2| f₂ | to be the left of L₂ , One can check that this satisfies lens equation for the third lens L₃