A convex lens of focal length 20 cm is placed in front of a convex… | JEE Main 2022 (25 Jul, Shift 2)

Q41JEE Main 2022 · 25 JUL · SHIFT 2Medium

Combination of Lenses

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ____________ cm.

Numerical answer type. Work it out, then open the answer.

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Answer: 10

Lens: $\frac{1}{v} = \frac{1}{20} - \frac{1}{60} = \frac{1}{30} \Rightarrow v = 30\text{ cm}$
Image coincides with the object, so rays hit the convex mirror normally: the lens image is at the mirror's centre of curvature.
$R = 30 - 10 = 20\text{ cm} \Rightarrow f = \frac{R}{2} = 10\text{ cm}$
Focal length of the convex mirror = 10 cm.

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