Question:
A person has a minimum distance of distinct vision of 50 cm. The power of lenses required to read a book at a distance of 25 cm is
A person has a minimum distance of distinct vision of 50 cm. The power of lenses required to read a book at a distance of 25 cm is
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For hypermetropic correction, you can directly use the simplified relation:
\[ P = 4 - \frac{100}{d} \]
where \( d \) is the person's actual near point in cm. Substituting \( d = 50 \text{ cm} \), we get \( P = 4 - \frac{100}{50} = 4 - 2 = 2 \text{ D} \). This formula directly gives the power needed to bring the near point from \( d \) back to \( 25 \text{ cm} \).
\[ P = 4 - \frac{100}{d} \]
where \( d \) is the person's actual near point in cm. Substituting \( d = 50 \text{ cm} \), we get \( P = 4 - \frac{100}{50} = 4 - 2 = 2 \text{ D} \). This formula directly gives the power needed to bring the near point from \( d \) back to \( 25 \text{ cm} \).
Updated On: May 28, 2026
- 3 D
- 1 D
- 2 D
- 5 D
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The person has a near point (minimum distance of distinct vision) of \( 50 \text{ cm} \), which means they cannot see objects clearly if they are closer than \( 50 \text{ cm} \). To read a book at the normal near point of \( 25 \text{ cm} \), they need a corrective lens that forms a virtual image of the book at their shifted near point.
Step 2: Key Formula or Approach:
We will use the classical lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( u \) is the object distance (\( -25 \text{ cm} \)).
- \( v \) is the image distance (\( -50 \text{ cm} \)).
- \( f \) is the focal length of the required lens.
- Power \( P \) of a lens in diopters (D) is given by \( P = \frac{1}{f \text{ (in meters)}} = \frac{100}{f \text{ (in cm)}} \).
Step 3: Detailed Explanation:
Using the Cartesian sign convention:
- Object distance, \( u = -25 \text{ cm} \)
- Image distance, \( v = -50 \text{ cm} \)
Substitute these values into the lens formula:
\[ \frac{1}{f} = \frac{1}{-50} - \frac{1}{-25} \]
\[ \frac{1}{f} = -\frac{1}{50} + \frac{1}{25} \]
\[ \frac{1}{f} = \frac{-1 + 2}{50} = \frac{1}{50 \text{ cm}} \]
Therefore, the focal length is:
\[ f = +50 \text{ cm} = 0.5 \text{ m} \]
The positive sign indicates that the required lens is a converging (convex) lens.
Now, calculate the power of the lens:
\[ P = \frac{1}{f \text{ (in meters)}} = \frac{1}{0.5 \text{ m}} = +2 \text{ D} \]
Step 4: Final Answer:
The power of the lens required is 2 D.
The person has a near point (minimum distance of distinct vision) of \( 50 \text{ cm} \), which means they cannot see objects clearly if they are closer than \( 50 \text{ cm} \). To read a book at the normal near point of \( 25 \text{ cm} \), they need a corrective lens that forms a virtual image of the book at their shifted near point.
Step 2: Key Formula or Approach:
We will use the classical lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( u \) is the object distance (\( -25 \text{ cm} \)).
- \( v \) is the image distance (\( -50 \text{ cm} \)).
- \( f \) is the focal length of the required lens.
- Power \( P \) of a lens in diopters (D) is given by \( P = \frac{1}{f \text{ (in meters)}} = \frac{100}{f \text{ (in cm)}} \).
Step 3: Detailed Explanation:
Using the Cartesian sign convention:
- Object distance, \( u = -25 \text{ cm} \)
- Image distance, \( v = -50 \text{ cm} \)
Substitute these values into the lens formula:
\[ \frac{1}{f} = \frac{1}{-50} - \frac{1}{-25} \]
\[ \frac{1}{f} = -\frac{1}{50} + \frac{1}{25} \]
\[ \frac{1}{f} = \frac{-1 + 2}{50} = \frac{1}{50 \text{ cm}} \]
Therefore, the focal length is:
\[ f = +50 \text{ cm} = 0.5 \text{ m} \]
The positive sign indicates that the required lens is a converging (convex) lens.
Now, calculate the power of the lens:
\[ P = \frac{1}{f \text{ (in meters)}} = \frac{1}{0.5 \text{ m}} = +2 \text{ D} \]
Step 4: Final Answer:
The power of the lens required is 2 D.
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