A boy can clearly see objects between distance 15 cm to 200 cm from his eye . To clearly see an object situated at infinity , what will be the power of the lens that should he use? If he wears that lens then what will be the least distance of distinct vision in that case?

Explanation

To see an object placed at infinity , focal length of the lens should be such that parallel rays coming from infinity seem to be coming from a point at a distance 200 cm .
`therefore 1/(-200)-1/oo=1/f or, f=-200 cm `
As f is negative , the lens is concave.
`therefore` Power of the lens , P`(100)/f=(100)/(-200)=-0.5 m^(-1)`
Let, while he is wearing spectacles, the least distance of distinct vision =u.
From the equation `1/v-1/u=1/f` we get
`1/(-15)-1/u=1/(-200) or, 1/u=-1/(15)+1/(200)=(-40+3)/(600) =-(37)/(600)`
or, `u=-(600)/(37)=-16.22 cm `
Hence , the required distance is 16.22 cm .