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 20cm from the first lens on the left, and the distance between the two lenses is 5cm. List II contains the positions of the final images.
List-I
List-II
(I)
(P)
Final image is formed at 7.5cm on the right side of lens 2.
(II)
(Q)
Final image is formed at 60.0cm on the right side of lens 2.
(III)
(R)
Final image is formed at 30.0cm on the left side of lens 2.
(IV)
(S)
Final image is formed at 6.0cm on the right side of lens 2.
(T)
Final image is formed at 30.0cm on the right side of lens 2.
Which one of the following options is correct?IIIIIIIV
(A)I→P, II→R, III→Q, IV→T✓ Correct
(B)I→Q, II→P, III→T, IV→S
(C)I→P, II→T, III→R, IV→Q
(D)I→T, II→S, III→Q, IV→R
Answer: (A)
Solution
(I) Lens 1 (f1=+10 cm), Lens 2 (f2=+15 cm):
Image from lens 1: v1=−20+10(−20)(10)=+20 cm
Object for lens 2: u2=+(20−5)=+15 cm
Image from lens 2: v2=15+15(15)(15)=+7.5 cm
I→P
(II) Lens 1 (f1=+10 cm), Lens 2 (f2=−10 cm):
v1=+20 cm, u2=+15 cm
v2=15−10(15)(−10)=−30 cm (left of lens 2)
II→R
(III) Lens 1 (f1=+10 cm), Lens 2 (f2=−20 cm):
v1=+20 cm, u2=+15 cm
v2=15−20(15)(−20)=+60 cm
III→Q
(IV) Lens 1 (f1=−20 cm), Lens 2 (f2=+10 cm):
v1=−20−20(−20)(−20)=−10 cm
u2=−(10+5)=−15 cm
v2=−15+10(−15)(10)=+30 cm
IV→T
Answer: (A) I→P, II→R, III→Q, IV→T
JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Single correct option
