Decoding the Optical Components
In this intriguing matrix match problem, we are tasked with pairing four distinct optical components with the types of images they can form for a real object placed on their principal axis. The components are a concave mirror, a convex mirror, a convex lens, and a silvered meniscus lens. Let's break down the physics behind each one.
The Versatile Concave Mirror
Component (A) is a standard concave mirror. A concave mirror is a converging optical system, which makes it incredibly versatile. Depending on where you place the real object, it can produce a wide variety of images:
Real Image: If the object is placed anywhere beyond the principal focus (u>f), the reflected rays converge to form a real, inverted image.
Virtual Image: If the object is placed very close to the mirror, between the pole and the focus (u<f), the reflected rays diverge. Extending them backwards yields a virtual, erect image.
Magnified Image: A magnified image is formed when the object is placed between the center of curvature and the focus (real and inverted) or between the pole and the focus (virtual and erect).
Image at Infinity: If the object is placed exactly at the principal focus (u=f), the reflected rays emerge parallel to each other, forming an image at infinity.
Thus, the concave mirror matches all four properties: p, q, r, s.
The Stubborn Convex Mirror
Component (B) is a convex mirror. Unlike its concave counterpart, a convex mirror is a diverging system. For any real object placed in front of it, the reflected rays will always diverge.
When these diverging rays are extended backwards, they always intersect between the pole and the principal focus behind the mirror. Consequently, a convex mirror always forms a virtual, erect, and diminished image. It can never form a real image, it can never magnify an object, and it can never form an image at infinity for a finitely placed real object.
Thus, the convex mirror matches only one property: q.
The Convex Lens
A Mirror's Twin
Component (C) is a convex lens. In the realm of refraction, a convex lens is the converging equivalent of a concave mirror. Its image formation cases are perfectly analogous:
Placing the object beyond the focus yields a real image.
Placing the object between the optical center and the focus yields a virtual image.
Placing the object between F and 2F, or between the optical center and F, yields a magnified image.
Placing the object exactly at the focus yields an image at infinity.
Thus, the convex lens matches all four properties: p, q, r, s.
The Silvered Lens
A Disguised Mirror
Component (D) is the trickiest of the bunch. It is a meniscus lens with its convex surface silvered. When one surface of a lens is silvered, the entire system behaves as an equivalent mirror. Light refracts through the front surface, reflects off the silvered back surface, and refracts again through the front surface.
The equivalent power of such a system is given by Peq​=2PL​+PM​. Because the silvered surface is convex (from the inside of the glass), it acts as a concave mirror. The overall system has a positive power, meaning it behaves as an effective concave mirror.
Since it acts as a concave mirror, it inherits all the versatile image formation properties we discussed in Case A. It can form real, virtual, magnified, and infinity images.
Thus, the silvered lens matches all four properties: p, q, r, s.
The Final Match
By carefully analyzing the converging or diverging nature of each optical component, we arrive at the final matrix match:
(A) → p, q, r, s
(B) → q
(C) → p, q, r, s
(D) → p, q, r, s
