Question

A cubical block of glass, refractive index 1.5, has a spherical cavity of radius `r=9cm` inside it as shown in figure . A luminous point object O is at a distance of 18cm from the cube. What is the apparent position of O as seen from A?

A. 17cm, left of `S_(4)`
B. 25cm, right of `S_(4)`
C. 13cm, left of `S_(4)`
D. 10cm, right of `S_(4)`

Answer 1

Correct Answer - a.
We have to consider four refractions at `S_(1),S_(2),S_(3) and S_(4)` respectively. At each refraction, we will apply single surface refraction equation.
For refractive at first surface `S_(1):`
`(3//2)/(upsilon_(1))-(1)/((-18))=0`
`upsilon_(1)=-27cm`
First image lies to the left of `S_(1)` .
For refractive at second surface `S_(2):`
`(1)/(upsilon_(2))-(3//2)/(-(27+9))=((1-3//2))/(+9)`
`upsilon_(2)=-(72)/(7)cm`
Note that origin of Cartesian coordinate system lies at vertex of surface `S_(2)`. The object distacne is `(27+9)cm` . The second image lies to left of `S_(2)`.
For refractive at third surface `S_(3):`
`u_(3)=-((72)/(7)+18)=-(198)/(7)`
`(1.5)/(upsilon_(3))-(1)/((-198//7))=((1.5-1))/((-9))`
`upsilon_(3)=-16.5cm`
For refractive at fourth surface `S_(4):`
`u_(4)=-(16.5+9)=-25.5cm`
`(1)/(upsilon_(4))-(3//2)/((-25.5))=((1-3//2))/(oo)=0`
`upsilon_(4)=-17cm`
The final image lies at 17cm to the left of surface `S_(4)`.