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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is

Asked in JEE Main Online 2017 · Focal length on the optical bench

Answer: (1) 27.5 cm

Step-by-step solution

Step 1: where would the lens alone send the light?

1/v-1/u=1/f with u=-20 cm, f=+15 cm.

1/v=1/(15)-1/(20)=(4-3)/(60)=1/(60), so v=60 cm behind the lens.

Step 2: the object and its image coincide only if the rays strike the mirror normally and retrace their path. That happens when the converging beam is heading for the mirror's centre of curvature.

The mirror is 5 cm behind the lens, so

R=60-5=55 cm.

Step 3: fₘᵢᵣᵣₒᵣ=R/2=(55)/2=27.5 cm.

Why the other options are wrong

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