Question

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
A		P	Final image is farmed at $7.5cm$ on the right side of lens 2 .
B		Q	Final image is formed at $60.0cm$ on the right side of lens 2.
C		R	Final image is formed at $30.0cm$ on the left side of lens 2.
D		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?

• 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

Answer 1

Answer: (A)

(I) $v_1=\frac{uf}{u+f}$
$=\frac{(-20)(10)}{(-20)+(10)}=+20$
$u_2=+15$
$v_2=\frac{(15)(15)}{(15)+(15)}=+7.5$
(II)$v_1=+20$
$u_2=+15$
$v_2=\frac{(15)(-10)}{(15)+(-10)}=-30$
(III) $v_1=+20$
$u_2=+15$
$v_2=\frac{(15)(-20)}{(15)+(-20)}=60$
(IV) $v_1=\frac{(-20)(-20)}{(-20)+(-20)}=-10$
$u_2=-15$
$v_2=\frac{(-15)(10)}{(-15)+(10)}=30$