A glass sphere, refractive index `1.5` and radius 10 cm, has a spherical cavity of radius 5 cm concentric with it. A narrow beam of parallel light is direccted into the sphere. Locate the final image.

Options

A. 25cm left of `S_(4)`, virtual
B. 25 cm right of `S_(4)` , real
C. 15 cm left of `S_(4)`, virtual
D. 20cm right of `S_(4)`, virtual

Answer

a.

Explanation

We will have single surface refractions successsively at the four surfaces `S_(1),S_(2),S_(3) and S_(4)`. Do not forget to shift origin to the vertex of respective surface.
Refractive at first surface `S_(1):` Light travels from air to glass.
`(1.5)/(upsilon_(1))-(1)/(oo)=((1.5-1))/((+10))`
`upsilon_(1)=30cm`
First image is object for the refractioni at second surface.
For refraction at surface `S_(2):` Light travels from glass to air.
`(1.5)/(upsilon_(2))-(1.5)/((+25))=(1-1.5)/((+5))`
`upsilon_(2)=-25cm`
For refraction at surface `S_(3):` Light travels from air to glass.
`(1.5)/(upsilon_(3))-(1)/((-35))=((1.5-1))/((-5))`
`upsilon_(3)=-35//3cm`
For refraction at surface `S_(4):` Light travels from glass to air
`(1)/(upsilon_(4))-(1.5)/(-(35//3+5))=(1-1.5)/(-10)`
The final image is virtual, formed at 25cm to the left of the vertex of surface `S_(4)`.