Given a thin convex lens (refractive index 2), kept in a liquid (refractive index 1, 1< 2) having radii of curvatures |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?
- ( 2+ 1)|R1|( 2- 1)
- 1|R1| |R2| 2 (2|R1|+|R2| )- 1 |R1| |R2|
- 1|R1| |R2| 2 (|R1|+|R2| )- 1|R1|
- 1|R1| |R2| 2 (|R1|+|R2| )- 1|R2|
Answer
(4) 1|R1| |R2| 2 (|R1|+|R2| )- 1|R2|
Solution
Silvered lens acts as a mirror (refraction, reflection, refraction): 1feq= 2f + 1fm
1f = ( 2- 1)(|R1|+|R2|) 1|R1||R2|, 1fm= 2|R2| 1feq= 2 [ 2(|R1|+|R2|)- 1|R2| ] 1|R1||R2|
[figure]
Real inverted image at the object's own place: object at the centre of curvature, u=2feq
u= 1|R1| |R2| 2 (|R1|+|R2| )- 1|R2|
Answer: (4)