Question

Lenses applied in achromatic combination having
dispersive power in ratio of 5:3 if focal length of
concave lens is 15 cm, then focal length of other
lens will be
(1)-9 cm
(2) +9 cm
(3) -12 cm (4)+12 cm​

Answer 1

Given,

ω

1

:ω

2

=5:3

f

1

=−15cm

We know that,

ω

2

ω

1

=−

f

2

f

1

. . . . . . .(1)

ω

2

ω

1

=

3

5

. . . . . .(2)

From equation (1) and equation (2), we get

−

f

2

f

1

=

3

5

f

2

=−

5

3f

1

f

2

=−

5

3×(−15cm)

=+9cm

Answer 2

Answer:

Answer will be 2nd

Explanation:

Now this question is very simple , there are two approaches for solving ,one long method and another short and simple ones , i will explain you the simple trick

See, in achromatic combination there are two lense one convex and another concave , now focal length of convex lens is positive , concave lens is negative ,

In question it is given that , focal length of concave Lens is 15 . So now just select the answer which will fit with 5 ratio 3

Like option 2

15/9 ratio is 5:3

Now the doubt how you can say that answer is 2nd , there are two option where answer is 9 with opposite signs,

You will have to select the +9 answer because , focal length of convex lens here written in question as " other lens " is always positive , so answer will be 2nd , hope you understand this , if you need more proper explanation then you can just ask me here .

Thank you