Question

A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices m₁ and m₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is
(a) $\frac{R}{2(\mu_{1}-\mu_{2})}$
(b) $\frac{R}{(\mu_{1}-\mu_{2})}$
(c) $\frac{2R}{(\mu_{2}-\mu_{1})}$
(d) $\frac{R}{2(\mu_{1}+\mu_{2})}$

Answer 1

(d) $\frac{R}{2(\mu_{1}+\mu_{2})}$

Answer 2

Answer:

R/( μ1- μ2)

Explanation:

The plano convex lens will fit exactly into the plano concave lens, with the plane surfaces parallel to each other

According to the lens maker formula - '/f = 1/f1 + 1/f2

1/f1 = (u-1) ( 1/∞ -1/-R)

= ( u1-1)/ R

1/f2 = (u2-1) ( 1/∞ -1/-R)

= ( u2-1)/ R

1/f = ( u1-1)/ R - ( u2-1)/ R

1/f = ( u1-u2)/R

f = R/( μ1- μ2)

Thus, the curved surface of the lenses, then the focal length of the combination is  R/( μ1- μ2),