A convex lens of focal length `f_(1)` is placed in front of a luminous point object. The separation between the object and the lens is `3f_(1)` . A glass slab of thikness t is placed between the object and the lens. A real image of the object is formed at the shortest possible distance from the object.
a. Find the refractive index of the slab.
b. If a concave lens of very large focal length `f_(2)` is placed in contact with the convex lens, find the shifting of the image.

Answer

(a) `(f)/(f-f_(2)) ` (b) `(4f_(1)^(2))/(f_(2))`

Explanation

a. For a convex lens, minimum distance between the object and image is 4f in which distance between the object and lens is 2f and between the lens and screen is 2f,
Hence, shifting `=3f_(1)-2f_(1)=f_(1)`
`s=t[1(1//mu))rArrmu=t(t-f_(1))`
b. `(1)/(F)=(1)/(f_(1))+(1)/((-f_(2))),(1)/(v')-(1)/(u)=(1)/(F),u=-2f_(1)`
`rArr v^(')=(2f_(1)f_(2))/(f_(2)-2f_(1))`
Shifting of image,
`s=v^(')-v=(2f_(1)f_(2))/(f_(2)-2f_(1))-2f_(1)`
`=(4f_(1)^(2))/(f_(2)-2f_(1))=(4f_(1)^(2))/(f_(2))` (as `f_(2)gt gtf_(1))`