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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. A. 25cm left of `S_(4)`, virtualB. 25 cm right of `S_(4)` , realC. 15 cm left of `S_(4)`, virtualD. 20cm right of `S_(4)`, virtual |
Answer» Correct Answer - a. 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)`. |
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