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A glass sphere, refractive index 1.5 and radius 10cm, has a spherical cavity of radius 5cm concentric with it. A narrow beam of parallel light is directed into the sphere. Find the final image and its nature. |
Answer» We will have single surface refractions successively at the four surfaces `S_(1), S_(2),S_(3)` and `S_(4)` . Do not forget to shift origin to vertex of the respective surface. Refractive at first surface `S_(1)` : Light travel from air to glass. `(1.5)/(upsilon_(1))-(1)/(oo)=((1.5-1))/((+1))` `upsilon_(1)=30cm`. First image is the object for the rafraction at second surface. For refractive at surface `S_(2):` Light travels from glass to air. `(1)/(upsilon_(2))-(1.5)/((+25))=(1-1.5)/((+5))` `upsilon _(2)=-25 cm` 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//3 cm` For refraction at surface `S_(4):` Light travels from glass to air. `(1)/(upsilon_(4))-(1.5)/(-(35//3+5))=(1-1.5)/(-10)` `upsilon_(4)=-25 cm` The final image is virtual, formed at 25 cm to the left of the vertex of surface `S_(4)`. |
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