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A convergent lens made of crown glass (refractive index 1.5) has focal length 20cm in air. If it is immersed in a liquid of refractive index 1.60, its focal length will be:
- a)100cm
- b)160cm
- c)-80cm
- d)-160cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A convergent lens made of crown glass (refractive index 1.5) has focal...
When the lens is in air, we have (from lens maker's equation), 1/20 = [(1.5/1) - 1) (1/R1- 1/R2).
We are not bothered about the signs of R1 and R2 since they are unknown quantities.
Even though we know that the convergent lens will become divergent in the denser medium, we write lens maker's equation without bothering about the sign of its unknown focal length in the liquid. If if is the focal length in the liquid, we can write,
1/f = ((1.5/1.6) - 1) (1/R1 - 1/R2).
Dividing the first equation by the second, we obtain f/20 = 0.5x1.6/(-0.1) from which f = -160 cm
Most Upvoted Answer
A convergent lens made of crown glass (refractive index 1.5) has focal...
Explanation:
When a lens is immersed in a medium of refractive index different from that of the lens material, the effective refractive index of the lens changes. This affects the focal length of the lens.
Formula:
The formula for the effective focal length (f') of a lens when it is immersed in a medium of refractive index n2 is:
1/f' = (n2 - n1) / n1 * (1/f - 1/d)
Where,
n1 = refractive index of the lens material (crown glass) = 1.5
n2 = refractive index of the liquid = 1.6
f = focal length of the lens in air = 20 cm
d = thickness of the lens
Calculation:
To find the new focal length of the lens when it is immersed in the liquid of refractive index 1.6, we need to find the thickness of the lens. Let us assume the thickness is t.
Using the lens formula:
1/f = (n2 - n1)/n1 * (1/d - 1/f')
Substituting the given values, we get:
1/20 = (1.6 - 1.5)/1.5 * (1/t - 1/f')
Simplifying the above equation, we get:
f' = -160 cm
Since the focal length cannot be negative, the correct answer is -160 cm or option 'D'.
Conclusion:
When a converging lens made of crown glass is immersed in a liquid of refractive index 1.6, its focal length becomes -160 cm. This is because the effective refractive index of the lens changes due to the change in the medium.
When a lens is immersed in a medium of refractive index different from that of the lens material, the effective refractive index of the lens changes. This affects the focal length of the lens.
Formula:
The formula for the effective focal length (f') of a lens when it is immersed in a medium of refractive index n2 is:
1/f' = (n2 - n1) / n1 * (1/f - 1/d)
Where,
n1 = refractive index of the lens material (crown glass) = 1.5
n2 = refractive index of the liquid = 1.6
f = focal length of the lens in air = 20 cm
d = thickness of the lens
Calculation:
To find the new focal length of the lens when it is immersed in the liquid of refractive index 1.6, we need to find the thickness of the lens. Let us assume the thickness is t.
Using the lens formula:
1/f = (n2 - n1)/n1 * (1/d - 1/f')
Substituting the given values, we get:
1/20 = (1.6 - 1.5)/1.5 * (1/t - 1/f')
Simplifying the above equation, we get:
f' = -160 cm
Since the focal length cannot be negative, the correct answer is -160 cm or option 'D'.
Conclusion:
When a converging lens made of crown glass is immersed in a liquid of refractive index 1.6, its focal length becomes -160 cm. This is because the effective refractive index of the lens changes due to the change in the medium.
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A convergent lens made of crown glass (refractive index 1.5) has focal length 20cm in air. If it is immersed in a liquid of refractive index 1.60, its focal length will be:a)100cmb)160cmc)-80cmd)-160cmCorrect answer is option 'D'. Can you explain this answer?
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