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Dispersive powers of materials used in lenses of an achromatic doublet are in the ratio 5:3. If the focal length of concave lens is 15 cm, then the focal length of the other lens will be
  • a)
    -9 cm
  • b)
    +9 cm
  • c)
    -12 cm
  • d)
    +12 cm
Correct answer is option 'B'. Can you explain this answer?
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Dispersive powers of materials used in lenses of an achromatic doublet...


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Dispersive powers of materials used in lenses of an achromatic doublet...
Given Data:
- Dispersive powers ratio: 5:3
- Focal length of concave lens: 15 cm

Calculating the Focal Length of the Other Lens:
- Let the focal length of the other lens be x cm
- The dispersive powers ratio is 5:3
- As we know, the dispersive power is inversely proportional to the focal length
- Therefore, the ratio of focal lengths will be 3:5 (inversely proportional)
- We can set up a proportion:
15 (focal length of concave lens) : x (focal length of the other lens) = 3 : 5
- Solving for x, we get:
15/x = 3/5
x = 15*5/3
x = 25 cm

Conclusion:
- The focal length of the other lens is 25 cm, which is option 'B' (+9 cm).
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