A thin equiconvex lens has focal length 10 cm and refractive index 1.5 . One of its faces is now silvered and for an object placed at a distance u in front of it, the image coincides with the object. The value of u is

Options

A. 20 cm
B. 10 cm
C. 5 cm
D. 20 cm

Answer

C

Explanation

Here image will be formed at its new focal length

This lens can be divident into two planoconvex lenses , `L_1` & `L_2`
As we know , focal length of planoconvex lens if its convex surface is polished is `F_1=R/"2u"`
`=R/(2xx1.5)=F_1=20/3` cm
Where R=20 cm & `mu`=1.5
Now, `F_2`=20 cm
So, `1/F=1/F_1+1/F_2`
`1/F=3/20+1/20=4/20` and `F=20/4`=5 cm