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Consider a transparent hemisphere (n=2) in front of which a small object is placed in air (n=1) as shown. What is the nature of final image of object x=2R |
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Answer» Erect & magnified TAKING refraction first at curve surface `2/v_(1)+1/x=1/R Rightarrow v_(1)=(2Rx)/(x-R)` for plane surface `v'=v_(1)-R Rightarrowv'=(xR+R^(2))/(x-R)Rightarrow1/v-(2(x-R))/(R(x+R))=0` `1/v=(2(x-R))/(R(x+R))` for virtual IMAGE `1/vlt0 Rightarrow(2(x-R))/(R(x+R))lt0` `xltR` (2)For`x=2R` `v_(1)=(4R^(2))/R=4R Rightarrow u=-2R` `m_(1)=mu_(1)/mu_(2).v/u=1/2. (4R)/((-2R))=-1` `m_(2)=1 Rightarrow m_(1)m_(2)=-1` Image is real inverted and same size. 
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