Converging mirrors facing each other

[jsalapide]

two converging mirrors A & B, having focal lengths 12 cm and 4 cm respectively, are facing each other and 36 cm apart on a common principal axis. A plastic sword is placed vertically upward in front of mirror A at a distance of 18 cm. Locate and describe the nature, orientation and size of the image formed by the combination of mirrors if the 12 cm mirror is the first reflector and reflection of light occurs only once on the surface of the mirrors.

First, I let the mirror A as the first reflector, I solved for q1 and I got 36. Therefore its a real image.

After that, I let the 2nd image at mirror B. To solve for p, I used p = d-q1, where d is the distance between the 2 mirrors. I got 0.

Is it possible for p to be zero? help..

 

[rl.bhat]

Yes. It is possible. A very small section of the any mirror acts like a plane mirror for which the object distance is the equal to image distance.

 

[tomcue]

I would approach this problem by first checking my calculations and assumptions to ensure their accuracy. If the calculations are correct, then it is possible for p to be zero in this scenario. This would mean that the image formed by the combination of the two mirrors is located at the surface of mirror B.

In terms of the nature and orientation of the image, it would be a real image since it is formed by the actual convergence of light rays. The orientation of the image would be inverted since the object (plastic sword) is placed in front of the mirror, and the image formed is located behind the mirror.

As for the size of the image, it would depend on the magnification of the mirrors. Since the focal length of mirror B is shorter than that of mirror A, the image formed by mirror B would be larger than the one formed by mirror A. However, without knowing the specific magnification of each mirror, it is difficult to determine the exact size of the image.

In conclusion, the combination of two converging mirrors facing each other can produce a real, inverted image at the surface of the second mirror, with its size dependent on the magnification of the mirrors.