A plano-convex lens of material of refractive | vedclass

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Question

(A) For a plano-convex lens with refractive index $\mu_1$ and radius of curvature $R$,the focal length $f_1$ is given by the lens maker's formula: $1/

Vedclass · Accepted Answer

$R/(\mu_1 - \mu_2)$

Vedclass · Answer

(A) For a plano-convex lens with refractive index $\mu_1$ and radius of curvature $R$,the focal length $f_1$ is given by the lens maker's formula: $1/f_1 = (\mu_1 - 1)(1/R - 1/\infty) = (\mu_1 - 1)/R$.For a plano-concave lens with refractive index $\mu_2$ and radius of curvature $R$,the focal length $f_2$ is given by: $1/f_2 = (\mu_2 - 1)(-1/\infty - 1/R) = -(\mu_2 - 1)/R$.When the two lenses are combined,the effective focal length $F$ is given by $1/F = 1/f_1 + 1/f_2$.Substituting the values: $1/F = (\mu_1 - 1)/R - (\mu_2 - 1)/R = (\mu_1 - 1 - \mu_2 + 1)/R = (\mu_1 - \mu_2)/R$.Therefore,the focal length of the combination is $F = R/(\mu_1 - \mu_2)$.

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