JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2022
- Medium
- Numerical
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 \(...cm\).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
For lens
\(\frac{1}{ v }-\frac{1}{ u }=\frac{1}{ f }\)
\(\Rightarrow \frac{1}{ v }-\frac{1}{(-60)}=\frac{1}{20} \Rightarrow \frac{1}{ v }+\frac{1}{60}=\frac{1}{20}\)
\(v =30\,cm\)
For final image to be formed on the objectitself, after refraction from lens the ray should meet the mirror perpendicularly and the image by lens should be on the centre of curvature of mirror
\(R =30-10=20\,cm\)
Focal length of mirror \(= R / 2=10\,cm\)
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