A rectangular glass block of thickness 10 cm and refractive index 1.5 placed over a small coin. A beaker is filled with water of refractive index `4//3` to a height of 10 cm and is placed over the glass block.
(a) Find the apparent position of the object when it is viewed at near normal incidence.
(b) if the eye is slowly moves away from the normal at a certain position, the object is found to disappear, due to total internal reflection. At what surface does this happen and why ?

Explanation

(a) Total shift
`OI=t_1(1-1//mu_1)+t_2(1-1//mu_2)`
`=10(1-(1)/(3//2))+10(1-(1)/(4//3))`
`=10/3+10/4`
Distance of image from P
`PI=PO-OI=(10+10)-(10/3+10/4)`
`=14.17cm`
(b) The image of coin disappears when the ray suffers T.I.R. at either at AB or CD.
The critical angle for galss-water surface
`mu_1sinC_1=mu_2sin90^@`
`3/2sinC_1=4/3`
`sinC_1=8/9`
`C_1=sin^-1(8//9)=sin^-1(0.88)`
The critical angle for water-air surface
`mu_2sinC_2=1xxsin90^@`
`4/3sinC_2=1`
`sinC_2=3/4`
`C_2=sin^-1(0.75)`
`C_2gtC_1`, T.I.R. occurs earlier at the water-air surface as eye is moved away from the normal.