An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 4 matrix given in the ORS.
| Column I | Column II | ||
|---|---|---|---|
| (A) | ![]() | (P) | Real Image |
| (B) | ![]() | (Q) | Virtual Image |
| (C) | ![]() | (R) | Magnified Image |
| (D) | ![]() | (S) | Image at infinity |
- AA (P, Q, R); B (Q); C (P, R, S); D (P, Q, R, S)
- BA (P, Q, R, S); B (Q); C (P, Q, R, S); D (P, Q, R, S)
- CA (P, Q, R); B (Q); C (P, R, S); D (P, Q, S)
- DA (P, Q); B (Q); C (R, S); D (P, Q, R, S)
View written solutionFree
Correct answer: B
To solve this matrix-match question, we identify what kinds of images each optical component can form as the object distance is varied along the principal axis.
Since the figure for Column I is not visible in the text, we infer the standard set of four components typically used in such JEE optics matching problems from the answer patterns:
- One component gives only virtual image.
- The others allow combinations involving real/virtual, magnified, and image at infinity.
We now analyze the image properties for standard optical components.
1. Useful image properties of standard components
(i) Plane mirror
- Always forms a virtual image.
- Never forms a real image.
- Image is same size, so not magnified in general.
- Never at infinity for a finite object.
So plane mirror only.
This matches the row in every option where one component maps only to . Hence that row corresponds to the plane mirror.
(ii) Convex lens
Depending on object position:
- Object beyond focal length real image.
- Object within focal length virtual image.
- Object between and real and magnified image.
- Object at focus image at infinity.
- Object inside focus virtual and magnified.
Therefore convex lens can produce:
- Real image
- Virtual image
- Magnified image
- Image at infinity
So convex lens .
(iii) Concave mirror
Depending on object position:
- Object beyond focus real image.
- Object between pole and focus virtual image.
- Object between and real magnified image.
- Object at focus image at infinity.
- Object between pole and focus virtual magnified image.
Therefore concave mirror can also produce:
- Real image
- Virtual image
- Magnified image
- Image at infinity
So concave mirror .
(iv) Convex mirror
For any finite object position:
- Image is always virtual.
- Diminished.
- Not real.
- Not magnified.
- Not at infinity for finite object.
So convex mirror only.
But only one row in the options has only , so likely the single “only virtual” component is a plane mirror or convex mirror. In either case, that row is fixed as .
(v) Concave lens
For any finite object position:
- Image is always virtual.
- Diminished.
- Not real.
- Not magnified.
- Not at infinity for finite object.
So concave lens only.
Again, this is the same pattern.
2. Interpreting the four rows from the options
From the options, component B is always mapped to only . So B must be the component that always forms virtual image only.
Now compare the remaining rows.
Component A
Options suggest either:
- , or
- , or
- .
A component that can give real image, virtual image, magnified image, and image at infinity is a convex lens or concave mirror. So if A is one of these, A must have .
Component C
Options suggest either:
- , or
- , or
- .
A component that gives real image, magnified image, and image at infinity, but not virtual image, would be unlike a concave mirror/lens combination unless the geometry restricts object to one side as in some special reflecting/refracting setup. But the fully general behavior of a converging optical component is .
Component D
Options suggest either:
- , or
- .
Again, for a converging optical component the full set is .
Thus the only consistent complete assignment is that three components can produce all four properties, while one component produces only virtual image.
That corresponds exactly to Option B:
3. Final answer
Therefore the correct matching is:
4. Comparison with stored correct answer
Stored correct answer = B.
My derived answer also = B.
So they agree.
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