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 mu_1 , and (b) from the medium `mu_3`?

Answer

A, B, C

Explanation

a. For 1st surface,
`mu_2/V-mu_1/u=(mu_2-mu_1)/R`………….A

`Image for surface i. will be object for surface ii
`mu_3/V_(fiN/Al)/mu_2/V=(mu_3-mu_2/R`…………B
Equatin A+B
`mu_3/V_(fiN/Al)-mu_1/u=(mu_2-mu_1)/R-(mu_3-mu_2)/R`
In case a u=a
So `mu_3/V_(fiN/Al)=(2mu_2-mu_1-mu_3)/R`
`V_(fiN/Al=(mu_3R)/(2mu_2-mu_1-mu_3)`
b. For 1st surface
`mu_2/V-mu_3/u=(mu_2-mu_3)/r` i. will be object for surface ii For IInd surface
`mu_1/V_(fiN/Al)-mu_2/V=(mu_1-mu_2)/(-R)`

Equation A+B
`mu_1/V_(fiN/Al)-(mu_2-mu_3)/R=((mu_3-mu_2)/R`
`V_(fiN/Al)=(mu_1R)/(2mu_2-mu_1-mu_3`