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Two lenses, with focal length f1 and f2, when combined produces no diffraction of light. If the ratio of the focal length f1 : f2 is 3 : 5. What will be the ratio of the dispersive power of the materials of the two lenses?
- a)3 : 5
- b)5 : 3
- c)25 : 9
- d)9 : 25
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two lenses, with focal length f1 and f2, when combined produces no dif...
Solution:
Given: The ratio of the focal length f1 : f2 is 3 : 5
Let the dispersive powers of the two lenses be D1 and D2 respectively.
We know that the dispersive power of a material is inversely proportional to its focal length.
Therefore, we can write:
D1 ∝ 1/f1
D2 ∝ 1/f2
Also, we know that when the lenses are combined, there is no diffraction of light. This implies that the combined lens behaves as a single lens with focal length given by:
1/f = 1/f1 + 1/f2
Substituting the given ratio of f1 : f2 in the above equation, we get:
1/f = 1/3f + 1/5f
Solving for f, we get:
f = 15/8 f
Now, using the relation between dispersive power and focal length, we can write:
D1/D2 = (1/f2)/(1/f1)
D1/D2 = f1/f2
D1/D2 = 3/5
Therefore, the ratio of the dispersive power of the materials of the two lenses is 3 : 5.
Hence, option A is the correct answer.
Given: The ratio of the focal length f1 : f2 is 3 : 5
Let the dispersive powers of the two lenses be D1 and D2 respectively.
We know that the dispersive power of a material is inversely proportional to its focal length.
Therefore, we can write:
D1 ∝ 1/f1
D2 ∝ 1/f2
Also, we know that when the lenses are combined, there is no diffraction of light. This implies that the combined lens behaves as a single lens with focal length given by:
1/f = 1/f1 + 1/f2
Substituting the given ratio of f1 : f2 in the above equation, we get:
1/f = 1/3f + 1/5f
Solving for f, we get:
f = 15/8 f
Now, using the relation between dispersive power and focal length, we can write:
D1/D2 = (1/f2)/(1/f1)
D1/D2 = f1/f2
D1/D2 = 3/5
Therefore, the ratio of the dispersive power of the materials of the two lenses is 3 : 5.
Hence, option A is the correct answer.
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Community Answer
Two lenses, with focal length f1 and f2, when combined produces no dif...
For no dispersion:
The negative shows that the nature of the dispersive power should be opposite in nature.
Therefore, the ratio of the dispersive powers of the material of the lenses will be 3 : 5.
Therefore, it is the correct option.
The negative shows that the nature of the dispersive power should be opposite in nature.
Therefore, the ratio of the dispersive powers of the material of the lenses will be 3 : 5.
Therefore, it is the correct option.
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Two lenses, with focal length f1 and f2, when combined produces no diffraction of light. If the ratio of the focal length f1 : f2 is 3 : 5. What will be the ratio of the dispersive power of the materials of the two lenses?a)3 : 5b)5 : 3c)25 : 9d)9 : 25Correct answer is option 'A'. Can you explain this answer?
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