A thin biconvex lens is prepared from the glass $(\mu =1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of _________ cm .

[JEE Main 2026, 8 Apr (Shift 2)]

Question

A thin biconvex lens is prepared from the glass $(\mu =1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of _________ cm .

[JEE Main 2026, 8 Apr (Shift 2)]

YESPYQ · Accepted Answer

Correct answer: a) 10. For the biconvex lens: ${f}_{L}=\frac{R}{2(\mu -1)}=\frac{20}{2(1.5-1)}=20cm$ For the silvered left surface, the mirror focal length is ${f}_{m}=\frac{R}{2}=-10cm$ For lens plus mirror combination: $\frac{1}{f}=\frac{1}{{f}_{m}}-\frac{2}{{f}_{L}}$ $\frac{1}{f}=-\frac{1}{10}-\frac{2}{20}=-\frac{1}{5}$ $f=-5cm$ For the image to coincide with the object, the object must be at the center of curvature of the equivalent mirror system: $u=2|f|=10cm$

A thin biconvex lens is prepared from the glass \((\mu =1.5)\) both curved surfaces of which have equal radii of 20 cm e…

Practice more JEE Physics PYQs