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A glass sphere of refractive index 1.5 forms the real image of object O at point I as shown in the figure when kept in air of refractive index 1. If the value of x is kR. Find k

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Solution :We can REVERSE the question. Let `I` BEHAVES as object and `O` behaves as image, because retracing the path will not later the DISTANCES.
Consider first refraction at point `N`
`1.5/V-1.0/(-R)=(1.5-1.0)/(+R)implies1.5/v=1/(2R)-1/Rimpliesv=-3R`

Consider second refraction at point `M`, for this `I`, wil behaves normal object so
`1.0/v-1.5/(-5R)=(1.0-1.5)/(-R)`
`implies1/v+3/(10R)=1/(2R)=5/(10R)`
`implies 1/v=5/(10R)-3/(10R)=1/(5R)`
`implies v=5R`
`impliesx=5Rimpliesk=5`


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