The dispersive powers of two lenses are 0.01 | vedclass

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(A) For an achromatic combination of two thin lenses in contact,the condition is given by: $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where $\o

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Diverging lens having focal length $20\, cm$.

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(A) For an achromatic combination of two thin lenses in contact,the condition is given by: $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$,where $\omega_1, \omega_2$ are the dispersive powers and $f_1, f_2$ are the focal lengths of the two lenses.Given: $\omega_1 = 0.01$,$\omega_2 = 0.02$,and $f_1 = +10\, cm$.Substituting the values into the condition: $\frac{0.01}{10} + \frac{0.02}{f_2} = 0$.$\frac{0.01}{10} = -\frac{0.02}{f_2}$.$f_2 = -\frac{0.02 	imes 10}{0.01} = -20\, cm$.The negative sign indicates that the second lens must be a diverging (concave) lens with a focal length of $20\, cm$.

The dispersive powers of two lenses are $0.01$ and $0.02.$ If the focal length of one lens is $+10\, cm$,what should be the focal length of the second lens so that they form an achromatic combination?

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