A thin lens made of a material of refractive index`mu_2` has a medium of refractive index `mu_1` on one side and a medium of refractive index on the other side. The lens is biconvex and the two radii of curvature have equal magnitude R. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed if the beam is incident from (a) the medium p, and (b) from the medium `mu_3`?

Answer

(a) `(mu_(3)R)/(2 mu_(2) - mu_(1) - mu_(3))`, (b) `(mu_(1)R)/(2mu_(2) - mu_(1) - mu_(3))`

Explanation

(a) For first refractiobn `(mu_(2))/(v_(1)) - (mu_(1))/(-oo) = (mu_(2) - mu_(1))/(R)`
`rArr v_(1) = (mu_(2) R)/(mu_(2) - mu_(1))`
for second refraction, this image is object.
`(mu_(3))/(v) - (mu_(2))/(v_(1)) = (mu_(3) - mu_(2))/(-R)`
`rArr (mu_(3))/(v) - (mu_(2) - mu_(1))/(R) = (mu_(2) - mu_(3))/(R) rArr (mu_(3))/(v) = (2mu_(2) - mu_(1) - mu_(3))/(R') rArr v = (mu_(3) R)/(2mu_(2) - mu_(1) - mu_(3))`
(b) By interchanging `mu_(1)` and `mu_(3), v = (mu_(1) R)/(2mu_(2) - mu_(3) - mu_(1))`