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In the figure given below a hemisphere m...

In the figure given below a hemisphere made of glass `(mu = 1.5)` is shown. Find the location of final image for the object O placed at a distance 40 cm from point P on the hemisphere. Consider outside medium as air.

Text Solution

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There will be two refractions. One from air to glass and then from glass to air. Let us first solve the refraction from air to glass.
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`rArr" "(1.5)/(v)-(1)/(-40)=(1.5-1)/(+40)`
`rArr" "(1.5)/(v)=(1)/(80)-(1)/(40)`
`rArr" "(1.5)/(v)=-(1)/(80)rArr v=-120cm`
Hence, this image will be at a distance 160 cm from the plane surface. And refraction will be from glass to air.
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`rArr" "(1.5)/(v)-(1)/(-40)=(1.5-1)/(+40)`
`rArr" "(1.5)/(v)=-(1)/(80)rArr v=-120cm`
Hence, this image will be at a distance 160 cm from the plane surface. And refraction will be from glass to air.
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`(1)/(v)-(1.5)/(-160)=(1-1.5)/(oo)`
`v=-(160)/(1.5)=-106.7cm`
Following is the ray diagram :
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