1.

Findout the equivalent focal length of the combenation of lenses shown in the figure. Surrounding medium is air.

Answer»

Solution :`1/f =1/v-1/u`
`rArr 1/10=1/v+1/15`
`rArr 1/v=1/10-1/15`
`rArr v=150/5=30`
`1/f=1/v-1/u`
By differentating :
`0=(dv)/(v^(2) dt)-(du)/(dt u^(2))`
`rArr 0=- (dv)/v^(2)+(du)/u^(2)`
`rArr (du)/u^(2)=(dv)/v^(2)`
`rArr (dv)/(du)=v^(2)/u^(2)`
`rArr dv =((30)^(2))/((15)^(2))xx(1-2)=-4(1)`
`rArr (v_(I)-v_(L))=v^(2)/u^(2) (v_(E)-v_(L))`
`rArr (v_(I)-2)=4xx-1`
`rArr v_(I)=-2`


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