Question

21. 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 u, and u, and R is the radius
of curvature of the curved surface of the lenses, then
the focal length of the combination is [NEET-2013]​

Answer 1

pls refer the attachment

I hope hope this helps ( ╹▽╹ )

Answer 2

Explanation:

Lens maker formula:

f

1

=(μ−1)(

R

1

1

−

R

2

1

) .......(1)

For Plano-convex lens: R

1

=∞ R

2

=−R

Using (1),

f

1

1

=(μ

1

−1)(

∞

1

−

−R

1

) ⟹

f

1

1

=

R

μ

1

−1

For Plano-concave lens: R

1

=−R R

2

=∞

Using (2),

f

2

1

=(μ

2

−1)(

−R

1

−

∞

1

) ⟹

f

2

1

=

R

1−μ

2

Thus focal length of combination,

F

1

=

f

1

1

+

f

2

1

=

R

μ

1

−1

+

R

1−μ

2

⟹ F=

μ

1

−μ

2

R