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A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal length
- a)Increases by a factor of 1.25
- b)Increases by a factor of 2.5
- c)Increases by a factor of 1.2
- d)Decreases by a factor of 1.2
Correct answer is option 'B'. Can you explain this answer?
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A lens is made of flint glass (refractive index = 1.5). When the lens...
The focal length of a lens is determined by the refractive indices of the lens material and the surrounding medium. When a lens is immersed in a liquid with a different refractive index, the focal length changes.
In this case, the lens is made of flint glass with a refractive index of 1.5, and it is immersed in a liquid with a refractive index of 1.25. We need to determine how the focal length changes in this scenario.
When a lens is immersed in a medium with a lower refractive index, the focal length increases. This is because the light rays passing through the lens bend less when they transition from the lens material to the surrounding medium. As a result, the lens has a longer focal length.
To calculate the exact change in focal length, we can use the lensmaker's equation:
1/f = (n - 1) * (1/R1 - 1/R2)
Where:
- f is the focal length of the lens
- n is the refractive index of the lens material
- R1 and R2 are the radii of curvature of the lens surfaces
Since we are only interested in the change in focal length, we can ignore the radii of curvature and focus on the refractive indices:
Δf/f = (Δn/n) * (1 - (n - 1)/n)
Where:
- Δf is the change in focal length
- Δn = n1 - n2 is the change in refractive index
- n1 is the refractive index of the lens material (flint glass)
- n2 is the refractive index of the surrounding liquid
In this case, n1 = 1.5 and n2 = 1.25. Plugging these values into the equation, we get:
Δf/f = (1.5 - 1.25)/1.5 * (1 - (1.5 - 1)/1.5) = 0.25/1.5 * (1 - 0.5/1.5) = 0.25/1.5 * (2/3) = 0.1667 * 0.6667 = 0.1111
This means that the focal length increases by approximately 0.1111 times its original value. To express this as a factor, we take the reciprocal of the change in focal length:
Factor = 1/(1 + Δf/f) = 1/(1 + 0.1111) = 1/1.1111 ≈ 0.9
Therefore, the focal length increases by a factor of approximately 0.9, which is equivalent to a decrease by a factor of 1/0.9 ≈ 1.1111.
Since none of the given options match this result, it appears that there is a mistake in the question or the answer choices.
In this case, the lens is made of flint glass with a refractive index of 1.5, and it is immersed in a liquid with a refractive index of 1.25. We need to determine how the focal length changes in this scenario.
When a lens is immersed in a medium with a lower refractive index, the focal length increases. This is because the light rays passing through the lens bend less when they transition from the lens material to the surrounding medium. As a result, the lens has a longer focal length.
To calculate the exact change in focal length, we can use the lensmaker's equation:
1/f = (n - 1) * (1/R1 - 1/R2)
Where:
- f is the focal length of the lens
- n is the refractive index of the lens material
- R1 and R2 are the radii of curvature of the lens surfaces
Since we are only interested in the change in focal length, we can ignore the radii of curvature and focus on the refractive indices:
Δf/f = (Δn/n) * (1 - (n - 1)/n)
Where:
- Δf is the change in focal length
- Δn = n1 - n2 is the change in refractive index
- n1 is the refractive index of the lens material (flint glass)
- n2 is the refractive index of the surrounding liquid
In this case, n1 = 1.5 and n2 = 1.25. Plugging these values into the equation, we get:
Δf/f = (1.5 - 1.25)/1.5 * (1 - (1.5 - 1)/1.5) = 0.25/1.5 * (1 - 0.5/1.5) = 0.25/1.5 * (2/3) = 0.1667 * 0.6667 = 0.1111
This means that the focal length increases by approximately 0.1111 times its original value. To express this as a factor, we take the reciprocal of the change in focal length:
Factor = 1/(1 + Δf/f) = 1/(1 + 0.1111) = 1/1.1111 ≈ 0.9
Therefore, the focal length increases by a factor of approximately 0.9, which is equivalent to a decrease by a factor of 1/0.9 ≈ 1.1111.
Since none of the given options match this result, it appears that there is a mistake in the question or the answer choices.
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A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer?
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A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer?.
A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lens is made of flint glass (refractive index = 1.5). When the lens is immersed in a liquid of refractive index 1.25, the focal lengtha)Increases by a factor of 1.25b)Increases by a factor of 2.5c)Increases by a factor of 1.2d)Decreases by a factor of 1.2Correct answer is option 'B'. Can you explain this answer?.
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