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Geometrical Optics question

2008 · Shift 2 · Q65
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Geometrical Optics question

2008 · Shift 2 · Q65

JEE AdvancedPhysicsGeometrical OpticsMCQ+4 / −1

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 ×\times× 4 matrix given in the ORS.

Column I Column II
(A) IIT-JEE 2008 Paper 2 Offline Physics - Geometrical Optics Question 14 English 1 (P) Real Image
(B) IIT-JEE 2008 Paper 2 Offline Physics - Geometrical Optics Question 14 English 2 (Q) Virtual Image
(C) IIT-JEE 2008 Paper 2 Offline Physics - Geometrical Optics Question 14 English 3 (R) Magnified Image
(D) IIT-JEE 2008 Paper 2 Offline Physics - Geometrical Optics Question 14 English 4 (S) Image at infinity

  1. A
    A →\to→(P, Q, R); B →\to→(Q); C →\to→(P, R, S); D →\to→(P, Q, R, S)
  2. B
    A →\to→(P, Q, R, S); B →\to→(Q); C →\to→(P, Q, R, S); D →\to→(P, Q, R, S)
  3. C
    A →\to→(P, Q, R); B →\to→(Q); C →\to→(P, R, S); D →\to→(P, Q, S)
  4. D
    A →\to→(P, Q); B →\to→(Q); C →\to→(R, S); D →\to→(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 →(Q)\to (Q)→(Q) only.

This matches the row in every option where one component maps only to QQQ. Hence that row corresponds to the plane mirror.


(ii) Convex lens

Depending on object position:

  1. Object beyond focal length fff ⇒\Rightarrow⇒ real image.
  2. Object within focal length fff ⇒\Rightarrow⇒ virtual image.
  3. Object between fff and 2f2f2f ⇒\Rightarrow⇒ real and magnified image.
  4. Object at focus fff ⇒\Rightarrow⇒ image at infinity.
  5. Object inside focus ⇒\Rightarrow⇒ virtual and magnified.

Therefore convex lens can produce:

  • PPP Real image
  • QQQ Virtual image
  • RRR Magnified image
  • SSS Image at infinity

So convex lens →(P,Q,R,S)\to (P,Q,R,S)→(P,Q,R,S).


(iii) Concave mirror

Depending on object position:

  1. Object beyond focus FFF ⇒\Rightarrow⇒ real image.
  2. Object between pole and focus ⇒\Rightarrow⇒ virtual image.
  3. Object between FFF and CCC ⇒\Rightarrow⇒ real magnified image.
  4. Object at focus FFF ⇒\Rightarrow⇒ image at infinity.
  5. Object between pole and focus ⇒\Rightarrow⇒ virtual magnified image.

Therefore concave mirror can also produce:

  • PPP Real image
  • QQQ Virtual image
  • RRR Magnified image
  • SSS Image at infinity

So concave mirror →(P,Q,R,S)\to (P,Q,R,S)→(P,Q,R,S).


(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 →(Q)\to (Q)→(Q) only.

But only one row in the options has only QQQ, so likely the single “only virtual” component is a plane mirror or convex mirror. In either case, that row is fixed as QQQ.


(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 →(Q)\to (Q)→(Q) 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 (Q)(Q)(Q). So B must be the component that always forms virtual image only.

Now compare the remaining rows.

Component A

Options suggest either:

  • (P,Q,R)(P,Q,R)(P,Q,R), or
  • (P,Q,R,S)(P,Q,R,S)(P,Q,R,S), or
  • (P,Q)(P,Q)(P,Q).

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 (P,Q,R,S)(P,Q,R,S)(P,Q,R,S).

Component C

Options suggest either:

  • (P,R,S)(P,R,S)(P,R,S), or
  • (P,Q,R,S)(P,Q,R,S)(P,Q,R,S), or
  • (R,S)(R,S)(R,S).

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 (P,Q,R,S)(P,Q,R,S)(P,Q,R,S).

Component D

Options suggest either:

  • (P,Q,R,S)(P,Q,R,S)(P,Q,R,S), or
  • (P,Q,S)(P,Q,S)(P,Q,S).

Again, for a converging optical component the full set is (P,Q,R,S)(P,Q,R,S)(P,Q,R,S).

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:

  • A→(P,Q,R,S)A \to (P,Q,R,S)A→(P,Q,R,S)
  • B→(Q)B \to (Q)B→(Q)
  • C→(P,Q,R,S)C \to (P,Q,R,S)C→(P,Q,R,S)
  • D→(P,Q,R,S)D \to (P,Q,R,S)D→(P,Q,R,S)

3. Final answer

Therefore the correct matching is:

Option B\boxed{\text{Option B}}Option B​


4. Comparison with stored correct answer

Stored correct answer = B.

My derived answer also = B.

So they agree.

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