The diagram shows an equiconvex lens. What should be the condition on the refractive indices so that the lens becomes diverging?

Options

A. ` 2mu _ 2 gt mu _ 1 - mu _ 3 `
B. ` 2 mu _ 2 lt mu _ 1 + mu _ 3 `
C. ` 2 mu _2 gt 2 mu _ 1 - mu _ 3 `
D. ` 2 mu _ 2 gt mu _ 1 + mu _ 3 `

Answer

B

Explanation

` ( mu _ 3 ) / ( v ) - ( mu _ 1 ) / ( u ) = ( mu _ 2 - mu _ 1 ) /( R _ 1 ) + ( mu _ 3 - mu _ 2) /( R _ 2) `
` rArr ( mu _ 3 ) /( v ) - ( mu _ 1 ) /( oo) = ( mu _ 2 - mu _ 1 ) / ( R) + (mu _ 3 - mu _ 2)/((-R )) `
` ( mu _ 3 ) / ( v ) = ( mu _ 2 - mu _ 1 ) /( R) - (( mu _ 3 - mu_ 2))/ ( R) lt 0 `
` rArr ` For diverging nature ` v lt 0 `
` ( mu _ 2 - mu _ 1 ) /( R) lt ( mu_ 3 - mu _ 2 ) /( R) rArr 2 mu _ 2 lt mu_ 1 + mu _ 3 `