Unit 13: Geometric and Physical Optics
Weightage : 15–18%
Which of the following indicates the object distance \(S_o\) for which a spherical concave mirror of focal length \(f\) produces an upright image?
Correct Answer: \( \boxed{\mathrm{A}} \)
For a concave mirror, the mirror equation is
\( \dfrac{1}{f}=\dfrac{1}{S_o}+\dfrac{1}{S_i}. \)
When the object is placed inside the focal point, that is,
\( S_o<f, \)
the reflected rays diverge, and their extensions intersect behind the mirror, producing a virtual, upright, and magnified image.
If \(S_o=f\), the reflected rays are parallel and the image forms at infinity. For \(S_o>f\), the image is real and inverted.
Therefore, the concave mirror produces an upright image only when the object is located inside the focal length.
Hence, the correct answer is (A).
The figure above shows a convex mirror, its focal point \(F\), and its center of curvature \(C\).
Which of the rays shown above is correct for this mirror?
Correct Answer: \( \boxed{\mathrm{B}} \)
A convex mirror always causes reflected rays to diverge. The reflected rays appear to originate from a point behind the mirror.
The principal ray rules for a convex mirror are:
• A ray parallel to the principal axis reflects as if it came from the focal point \(F\).
• A ray directed toward the focal point reflects parallel to the principal axis.
• A ray directed toward the center of curvature \(C\) reflects back along its own path because it strikes the mirror normally.
Among the four rays shown, Ray 2 is the only one that correctly satisfies these reflection rules. Its reflected ray diverges while its backward extension passes through the appropriate point behind the mirror.
The other rays violate one or more of the principal ray rules for a convex mirror.
Therefore, the correct answer is (B).
For which of the following does one obtain an image of increased size from a real object? Take all focus and radius of curvature values as positive.
Correct Answer: \( \boxed{\mathrm{D}} \)
Evaluate each optical system:
(A) For a converging lens, an object placed beyond the center of curvature (\(d_o>2f\)) forms a real, inverted, and reduced image. Therefore, it is not magnified.
(B) A diverging lens always produces a virtual, upright, and reduced image of a real object, regardless of the object’s position.
(C) A concave lens is also a diverging lens and always forms a virtual, upright, and reduced image.
(D) For a concave mirror, when the object is located between the focal point and the center of curvature (\(f<d_o<2f\)), the image formed is real, inverted, and magnified.
A summary of the relevant cases:
• Converging lens with \(d_o>2f\): real, reduced.
• Diverging (concave) lens: always virtual and reduced.
• Concave mirror with \(f<d_o<2f\): real and magnified.
Therefore, only (D) produces an image of increased size from a real object.
