JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Geometrical Optics

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A convex lens of focal length 20 cm is placed in front of 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.

Answer: 10

Solution

For the convex lens, using the lens formula:

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\frac{1}{v} - \frac{1}{( - 60 )} = \frac{1}{20}

\frac{1}{v} = \frac{1}{20} - \frac{1}{60} = \frac{3 - 1}{60} = \frac{2}{60} = \frac{1}{30}

v = 30 cm

For the final image to coincide with the object, the rays must strike the mirror perpendicularly and reflect back along the same path. This happens when the image formed by the lens lies at the center of curvature of the mirror.

Distance of image from mirror =

30 - 10 = 20

cm = radius of curvature

R

Focal length of convex mirror:

f = \frac{R}{2} = \frac{20}{2} = 10

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Integer answer

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JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Geometrical Optics

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