Question

An object is placed at a distance of 20 cm from a coaxial combination of two lenses A and B in contact. The combination forms a real image three times the size of the object. If lens B is concave with a focal length of 48 cm, what is the nature and focal length of lens A ?

Answer 1

Answer:

convex, 6 cm

Explanation:

Given,

Object distance, u=10 cm

Real image ⇒ other ride ⇒v=+ve

Magnification, m+3⇒−

u

v

=3

So, v=−3u=−3×(−10)=30 cm

Combined focal constant =F

then

f

1

=

v

1

−

u

1

=

30

1

−

−10

1

=

30

1+3

=

30

4

⇒F=

2

15

cm

but

F

1

=

f

1

1

+

f

2

1

so

15

2

=

−30

1

+

f

2

1

Because concave f

1

=−30 cm on solving we get

30

4

+

30

1

=

f

2

1

⇒f

2

=6 cm +ve⇒ convex.

Answer 2

Answer:

Given,

Object distance, u=10 cm

Real image ⇒ other ride ⇒v=+ve

Magnification, m+3⇒−

u

v

=3

So, v=−3u=−3×(−10)=30 cm

Combined focal constant =F

then

f

1

=

v

1

−

u

1

=

30

1

−

−10

1

=

30

1+3

=

30

4

⇒F=

2

15

cm

but

F

1

=

f

1

1

+

f

2

1

so

15

2

=

−30

1

+

f

2

1

Because concave f

1

=−30 cm on solving we get

30

4

+

30

1

=

f

2

1

⇒f

2

=6 cm +ve⇒ convex.