The dispersive powers of crown and flint glas | vedclass

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Question

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

Vedclass · Accepted Answer

$-20$

Vedclass · Answer

(A) For an achromatic combination of two thin lenses in contact,the condition is given by $\frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0$.Here,$\omega_1 = 0.02$ (crown glass) and $\omega_2 = 0.04$ (flint glass).The focal length of the flint glass lens is $f_2 = 40 \ cm$.Substituting the values into the formula:$\frac{0.02}{f_1} + \frac{0.04}{40} = 0$$\frac{0.02}{f_1} = -\frac{0.04}{40}$$\frac{0.02}{f_1} = -0.001$$f_1 = -\frac{0.02}{0.001} = -20 \ cm$.Thus,the focal length of the crown glass lens is $-20 \ cm$.

The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

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