JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Geometrical Optics

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses

L_{1}

and

L_{2}

with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens

L_{1}

as shown in the figure. The distance between the object and the image formed by the system of two lenses is ______ cm.

Answer: 34

Solution

For the first lens

L_{1}

with focal length

f_{1} = 24

cm and object distance

u_{1} = - 6

cm:

Using lens formula:

\frac{1}{v _{1}} - \frac{1}{u _{1}} = \frac{1}{f _{1}}

\frac{1}{v _{1}} + \frac{1}{6} = \frac{1}{24}

\frac{1}{v _{1}} = \frac{1}{24} - \frac{1}{6} = - \frac{1}{8}

v_{1} = - 8

cm (virtual image 8 cm to the left of

L_{1}

)

For the second lens

L_{2}

, the object distance is

u_{2} = - (8 + 10) = - 18

cm:

\frac{1}{v _{2}} + \frac{1}{18} = \frac{1}{9}

\frac{1}{v _{2}} = \frac{1}{9} - \frac{1}{18} = \frac{1}{18}

v_{2} = 18

cm (real image 18 cm to the right of

L_{2}

)

Total distance from object to final image =

6 + 10 + 18 = 34

cm.

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Numerical answer