JEE PYQ: Ray Optics Question 23
Question 23 - 2020 (06 Sep Shift 1)
A point like object is placed at a distance of 1 m in front of a convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:
(1) 2.6 m from the mirror, real
(2) 1 m from the mirror, virtual
(3) 1 m from the mirror, real
(4) 2.6 m from the mirror, virtual
Show Answer
Answer: (4)
Solution
Focal length of the convex lens, $f = 0.5$ m Object is at 2$f$ so, image ($I_1$) will also be at 2$f$. Image of $I_1$ i.e., $I_2$ will be 1 m behind mirror. Now $I_2$ will be object for lens. $\therefore u = (-1) + (-1) + (-1) = -3$ m Using lens formula, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ $\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{+0.5} + \frac{1}{-3}$ or $v = \frac{3}{5} = 0.6$ m Hence, distance of image from mirror $= 2 + 0.6 = 2.6$ m and real.
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