Question

A converging pencil of rays passes through an opening in a screen, as shown in Fig.. The vertex of the pencil A lies 15 cm from the screen. How will the distance between the point of convergence of the rays and the screen change if a converging lens whose focal length is 30 cm is placed in the opening? 

 

Answer 1

Answer: It will move 5 cm closer to the screen.

Explanation:

In the calculation of the new position of the vertex of the pencil with the aid of the thin lens formula, the vertex A of the pencil should be considered as an object. In the usual case (a point object — the vertex of the diverging pencil of rays) the vertex lies on the same side of the lens as the incident rays; while in the case under consideration, the vertex and the incident rays are on opposite sides of the lens. Therefore, in the calculation, the distance a₁ to the object must be introduced into the thin lens formula with a negative sign, i.e., a₁ = — 15 cm. 

In the graphical construction, one should determine the path of the auxiliary rays BA and CA passing through the lens from the left, in the direction of point A. The point of intersection of these rays determines the new position of the vertex of the pencil A' (Fig.).