In Figure, a fish watcher watches a fish through a 3.0 cm thick glass wall of a fish tank. The watcher is in level with the fish, the index of refraction of the glass is `8//5` and that of the water `4//3` .
a. To the fish, how far away does the watcher appear to be ?
b. To the watcher, how far away does the fish appear to be ?

Answer

A, B, C, D

Explanation

`OA=8.0 cm`
`:. AI_1=(n_g)(OA)`
`=(8/5)(8.0)=12.8 cm`
For reflection at `EG(R=oo),` using

`(n_2)/v-(n_1)/u=(n_2-n_1)/R`
`:. (4//3)/(BI_2)-(8//5)/(-(12.8+3))=0`
`:. BI_2=-(15.8)(4//3)(5//8)=-13.2 cm`
`:. FI_2=13.2+6.8=20.0 cm`
For face EF

`(8//5)/(BI_1)-(4//3)/(-6.8)=0`
`:. BI_1=-(6.8)(8//5)(3//4)`
`=-8.16 cm`
For face CD
`1.0/(AI_2)-(8//5)/(-(11.16))=0`
`:. AI_2=-(11.16)(5//8)`
`=-6.975 cm`
`:. FI_2=8+6.975`
`=14.975 cm`