An object O is placed at 8cm in front of a glass slab, whose one face is silvered as shown in Figure. The thickness of the slab is 6cm. If the image formed 10 cm behind the silvered face, find the refractive index of glass.

Explanation

At first surface,
`(mu_(1))/(d_(1))-(mu_(2))/(d_(2))rArr (1)/((-8))=(mu_(2))/(d_(2))rArrd_(2)=-8mu`
Image `I_(1)` will serve as an object for the mirror and form an image `I_(2)` behind it at a distance of ` (8mu+6)` cm.
`I_(2)` will serve as an object for the first surface.
The rays will reflect from the mirror.
Again using `(d_(1)^('))/(mu)=(d_(2)^('))/(1)`
`d_(1)^(')=d_(2)+2t=(-8mu+12)`
`d_(2)^(')=-(10+6)=-16cm `
After substituting the values, `mu=1.5.`