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The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%?
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The refractive index of a lens material is 1.5 and focal length f.Due ...
**Given:**
Refractive index of lens material (n) = 1.5
Focal length (f) = f
**To find:**
Percentage change in focal length
**Solution:**
Let's assume the initial focal length of the lens is f₀.
The formula relating the refractive index (n) and focal length (f) is given by:
n = 1 / f₀
From the given information, we can write:
n = 1 / f₀₀ (where f₀₀ is the initial focal length)
The refractive index has increased by 2%, so the new refractive index is:
n' = 1.02 * n
Substituting the value of n from the first equation:
n' = 1.02 * (1 / f₀₀)
The new focal length (f₁) can be calculated using the new refractive index:
n' = 1 / f₁
Substituting the value of n' from the second equation:
1 / f₁ = 1.02 * (1 / f₀₀)
Now, we can solve this equation to find f₁:
f₁ = f₀₀ / 1.02
Let's calculate the percentage change in focal length:
Percentage change = ((f₁ - f₀₀) / f₀₀) * 100
Substituting the values:
Percentage change = ((f₀₀ / 1.02 - f₀₀) / f₀₀) * 100
Simplifying the equation:
Percentage change = ((f₀₀ - f₀₀ * 1.02) / f₀₀) * 100
Percentage change = ((f₀₀ - 1.02 * f₀₀) / f₀₀) * 100
Percentage change = (1 - 1.02) * 100
Percentage change = -2%
Therefore, the percentage change in the focal length of the lens is -2%, which is equivalent to -2/100 * 100 = -2%.
Hence, the correct option is 2) -4.5%.
Refractive index of lens material (n) = 1.5
Focal length (f) = f
**To find:**
Percentage change in focal length
**Solution:**
Let's assume the initial focal length of the lens is f₀.
The formula relating the refractive index (n) and focal length (f) is given by:
n = 1 / f₀
From the given information, we can write:
n = 1 / f₀₀ (where f₀₀ is the initial focal length)
The refractive index has increased by 2%, so the new refractive index is:
n' = 1.02 * n
Substituting the value of n from the first equation:
n' = 1.02 * (1 / f₀₀)
The new focal length (f₁) can be calculated using the new refractive index:
n' = 1 / f₁
Substituting the value of n' from the second equation:
1 / f₁ = 1.02 * (1 / f₀₀)
Now, we can solve this equation to find f₁:
f₁ = f₀₀ / 1.02
Let's calculate the percentage change in focal length:
Percentage change = ((f₁ - f₀₀) / f₀₀) * 100
Substituting the values:
Percentage change = ((f₀₀ / 1.02 - f₀₀) / f₀₀) * 100
Simplifying the equation:
Percentage change = ((f₀₀ - f₀₀ * 1.02) / f₀₀) * 100
Percentage change = ((f₀₀ - 1.02 * f₀₀) / f₀₀) * 100
Percentage change = (1 - 1.02) * 100
Percentage change = -2%
Therefore, the percentage change in the focal length of the lens is -2%, which is equivalent to -2/100 * 100 = -2%.
Hence, the correct option is 2) -4.5%.
Community Answer
The refractive index of a lens material is 1.5 and focal length f.Due ...
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The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%?
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The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%?.
The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The refractive index of a lens material is 1.5 and focal length f.Due to some chemical changes in the material it's refractive index has increased by 2%.The percentage change in its focal length is. 1) 4.5%. 2)-4.5%. 3) 5.67%. 4)-5.67%?.
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