JEE Advanced · Physics · 24. Ray Optics

List I contains four combinations of two lenses ( 1 and 2 ) whose focal lengths (in cm ) are indicated in the figures. In all cases, the object is placed 20 cm from the first lens on the left, and the distance between the two lenses is 5 cm . List II contains the positions of the final images.
List - I List - II
(I) (P) Final image is formed at 7.5 cm on the right side of lens 2.
(II) (Q) Final image is formed at 60.0 cm on the right side of lens 2.
(III) (R) Final image is formed at 30.0 cm on the left side of lens 2.
(IV) (S) Final image is formed at
6.0 cm on the right side of lens 2.
(T) Final image is formed at 30.0 cm on the right side of lens 2.
Which one of the following options is correct?

A $I \to P, II \to R, III \to Q, IV \to T$
B $I \to Q, II \to P, III \to T, IV \to S$
C $I \to P, II \to T, III \to R, IV \to Q$
D $I \to T, II \to S, III \to Q, IV \to R$

Verified Solution

Answer & Solution

Correct Answer

(A) $I \to P, II \to R, III \to Q, IV \to T$

Step-by-step Solution

Detailed explanation

u = - 20 cm

f_{1} = + 10 cm

Using the lens formula,

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is

0.5 mm

. The circular scale has

100

divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Measurement condition	Main scale reading	Circular scale reading
Two arms of gauge touching each other without wire	$0$ division	$4$ divisions
Attempt- $1$ : With wire	$4$ divisions	$20$ divisions
Attempt- $2$ : With wire	$4$ divisions	$16$ divisions

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

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	List-I		List-II
(i)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{j} + \cos ω t \hat{k})$	(p)	$0$
(ii)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{i} + \cos ω t \hat{j})$	(q)	$- \frac{α}{4} \hat{i}$
(iii)	$\frac{1}{\sqrt{2}} (\sin ω t \hat{i} + \cos ω t \hat{k})$	(r)	$\frac{3 α}{4} \hat{i}$
(iv)	$\frac{1}{\sqrt{2}} (\cos ω t \hat{j} + \sin ω t \hat{k})$	(s)	$\frac{α}{4} \hat{j}$
		(t)	$- \frac{3 α}{4} \hat{i}$

	List - I		List - II
(I)		(P)	Final image is formed at 7.5 cm on the right side of lens 2.
(II)		(Q)	Final image is formed at 60.0 cm on the right side of lens 2.
(III)		(R)	Final image is formed at 30.0 cm on the left side of lens 2.
(IV)		(S)	Final image is formed at 6.0 cm on the right side of lens 2.
		(T)	Final image is formed at 30.0 cm on the right side of lens 2.