Question

Consider a medium of refractive index 1.5 bounded by two spherical surfaces 111

and 222 as shown in fig. The radii of curvature of the two surfaces are 15 cm and

25 cm with the center of curvature 1 and 2 respectively. There is an object at a

distance of 40 cm on the line joining 1 and 2. Determine the position of paraxial

image.​

Answer 1

Explanation:

For spherical surfaces, the following relation holds good

v

μ

2

−

u

μ

1

=

R

μ

2

−μ

1

where,

μ

2

=Refractive index of glass

μ

1

=Refractive index of air

v=OP

u= OQ

Given that OP=2OQ (in magnitude, and opposite in sign)

OQ

1.5

−

OP

1

=

R

1.5−1

OQ

1.5

−

−2OQ

1

=

R

1.5−1

4R=OQ

OP=2OQ=2(4R)

⇒OP=8R